Of American-English origin, the phrase honest Injun, also honest Indian, is used as an interjection to assert—or as an interrogation to appeal to—truthfulness, honour or sincerity. It is also used as a subject complement meaning: truthful, honourable or sincere (cf., below, quotations 6 [?], 8 & 9).
—Synonym: Scout’s honour.

The phrase honest Injun occurs, for example, in the following dialogue from The Maestro, an episode, first broadcast on BBC1 on Monday 1^st February 2021, of the British television series The Mallorca Files— interrogated by Detective Miranda Blake, played by the Welsh actress Elen Rhys (born 1983), a suspect, played by the English actor Graeme Hawley (born 1975), declares:

I don’t know nothing about it, love. Honest Injun.

Linguistic note: Injun represents a pronunciation of Indian with assibilated /d/. (Likewise, Cajun represents a pronunciation of Acadian with apheresis and assibilated /d/.)

Now considered offensive, the phrase honest Injun, also honest Indian, perhaps alludes to the fact that, in their past interactions with Europeans, Native Americans had to give assurance of their good faith—the assumption by the former being that the the latter were untrustworthy.

The earliest occurrences of the phrase honest Injun, also honest Indian, that I have found are as follows, in chronological order:

1-: From the Buffalo Daily Courier (Buffalo, New York) of Saturday 26^th July 1851:

The Michigan Conspiracy Case.—The Detroit Advertiser reports the proceedings on the thirty-seventh day of this trial. The exertions of counsel for the defence continue to be devoted almost to the impeachment of Henry Phelps. No facts were elicited of sufficient importance for recapitulation. The candor of one of the witnesses was laughable:
S. Whitney, being sworn, said, I had some words with Phelps, after I got back from Oakland; I described the land to Phelps, and he told me I did not describe the land at all: I stuck to it that I had been on the land, but I lied about it, and he had the impudence to intimate it, and even say to me that I lied about it; I had a quarrel with him, this Spring, I think it was, but I am not certain; honest Indian, I can’t remember of ever having caught Phelps in a lie, but he has caught me in one here under oath: I don’t feel bound to tell the truth on all frivolous affairs.
Two hundred and eighteen witnesses have now been examined; ninety-seven for the prosecution, and one hundred and twenty-one for the defence.

2-: From California, in 1851. Letter Sixth. A Trip into the Mines, from Rich Bar, East Branch of the North Fork of Feather River, dated Tuesday 30^th September 1851, by ‘Shirley’, published in The Pioneer; or, California Monthly Magazine (San Francisco, California) of July 1854:

In the first part of my letter, I alluded to the swearing propensities of the Rich Barians. Those of course would shock you; but though you hate slang, I know that you could not help smiling at some of their bizarre cant phrazes [sic].
For instance, if you tell a Rich Barian anything which he doubts, instead of simply asking you if it is true, he will invariably cock his head interrogatively, and almost pathetically address you with the solemn adjuration, “Honest Indian?” Whether this phrase is a slur or a compliment to the aboriginees of this country, I do not know.

3-: From Ye Jersey Hunter, by ‘Larynx’, from Cincinnati, dated Monday 13^th April 1857, written for, and published in, Porter’s Spirit of the Times. A Chronicle of the Turf, Field Sports, Literature and the Stage (New York City, New York) of Saturday 23^rd May 1857:

“Well, Jersey, how many birds did you get?”
“Twenty!” was the nonchalant response.
“The devil, you did! Show ’em!”
Jersey showed ’em. Eight extremely indignant and revengeful looks.
“Jersey, honest injun. Did you really kill those birds?”
“Not one of ’em!”

4-: From the Weekly Trinity Journal (Weaverville, California) of Saturday 3^rd April 1858:

Why, Charles, we Did’nt!—The Nevada Journal says that Mr. De Long stated in the Assembly that the Nevada and Trinity Journals desired to have him strung up by the neck till he was d-e-a-d! That paper disclaims any such sanguinary suggestion for the little Assemblyman’s abatement. And we, most violently, vociferate that we would use our best razor to sever the rope into infinitessimal bits, by which we might, could or should find Mr. De Long suspended.—What! Hang the little giant, la petite statesman! Never, by all that’s indivisible—not while a pinfeather is to be found on the American eagle.—Hung be the heavens with black, and all creation be hanged, but a mildew and a rottenness on the hemp that may be growing to hang the little Assemblyman. No! nevaire, nev-aire! As soon would we adjudge strangulation for an infant cat with no guilt on its soul but original sin. Charles, we did’nt say hang, once; honest Injun. We appeal to posterity.

5-: From Report of a Sarmint Delivered at the “Smilin Mule,” by the Rev. Felix Drygripes, Mishonary to the Setlers on Whiskey Neck, written for, and published in, the Holt County News (Oregon, Missouri) of Friday 10^th September 1858:

O, Jubiter! Father of the gods and men! Long have I prayed to be relieved of this orful diseas; I have swallered all your Kollagogs, Hellagogs and other gogs, ’cept your thunderbolts and still my abdomenal functions toot out like a drapsy, and I have acumulated an ager kake into my side nigh unto as big as a yearlin mule.—Say old Fel. honest injun, now does this look like kuren a body? Now with your Magistys permission, I perpose to perform a maracle onto myself this day before my whole household, which shall remain as a inheritance to all the wandering generations of men, who found their cities onto the marshy grounds by the sea side, whar the Pestilens goeth down to drink on stilts every day about noon.

6-: From a correspondence from Rosecrans’ Army, Camp Sill, near Murfreesboro, dated Tuesday 10^th February 1863, published in the Chicago Daily Tribune (Chicago, Illinois) of Friday 20^th February 1863:

I made a second acquaintance with Paymaster’s former friend, Armistic, soon after the battle of Murfreesboro. So changed had he become in voice, attire and manners that I should have been warranted in turning him over to the watchful care of the P. G’s as an imposter had he not produced evidence of identity in a display of his well-thummed letters of introduction from his old employers, Messrs. Wood, Vallandigham, Bright, Richardson & Co. Added to these he has a haversack full of preambled resolutions, habeas corpus blanks, confidential letters from Hangman Foote, “one” Jefferson Davis, and a Kentucky “exile” of much obesity subscribing himself Hum. Marshall. He speaks in flowing terms of the spirited properties of Jersey cider and Western corn-juice, and not a rum palace or a whisky doggery exists in New York, Trenton, Indianapolis or Springfield, but he knows as familiarly and haunts as closely as a butcher’s dog does scrap-corner on killing days. Within Rosecrans’ army he is an object of curiosity and scorn, and his presence is only tolerated so long as his actions and disposition comport with those of a hired spy bribed to play “honest Injun” for both armies.

7 & 8-: From City News, published in The Leavenworth Daily Conservative (Leavenworth, Kansas):

7-: Of Tuesday 14^th April 1863:

Continued.—Quantrell’s photograph is still on exhibition at the Fort. Persons desirous of gazing upon that “human face divine” can be gratified by calling up. It looked well when we saw it. No picture was ever taken to better advantage—honest Injun.

8-: Of Tuesday 5^th May 1863:

Remember—That Messrs. Stettauer & Bro, for the purpose of closing out their present stock of goods, preparatory to the erection of a fine building on the old corner, are selling their splendid assortment of the latest styles of dry and dress goods at less than cost. There is no mistake about this, it’s “honest injun.” Call and see them, corner of Third and Delaware streets.

9-: From a correspondence from the Army of the Cumberland, near Bridgeport, Alaska, dated Wednesday 18^th November 1863, published in the Chicago Daily Tribune (Chicago, Illinois) of Thursday 26^th November 1863:

One of the common hallucinations to which a soldier is subject, is the impression that sheep and cattle are carnivorous animals, and that it is his bounden duty to shoot them if he has his musket, or to club them if he has it not. In an enemy’s country, and when short of rations, this singular mental derangement is productive of little harm, and officers wink at it. But where the Commissary furnishes plenty of hard bread and coffee, and pork and beans, and such luxuries, it does not seem quite “honest Indian” to slay graniverous [sic] animals under the mistaken notion that they are flesh eating and dangerous. It demoralizes the men and pains the good Union citizen.