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The expression hoop snake designates a mythical snake that puts its tail in its mouth and then rolls after its intended victim.
—Also, occasionally: horn snake, with reference to a horny sting in the snake’s tail (cf. below, quotations 1 & 3).

The expression hoop snake occurs, for example, in the following from Australian Army: The Soldiers’ Newspaper (Canberra, Australian Capital Territory, Australia) of Thursday 9^th December 1976 [page 7, column 4]:

Silver City was missing at the . . .
Silver ceremonial at Kapooka

THE 1^st Recruit Training Battalion, Kapooka, was 25 years old last month.
[…]
With 25 years of history behind the 1^st Recruit Training Battalion, many soldiers who passed out from 1 RTB will remember the legends and stories of drop bears and hoop snakes that supposedly originated there.

The earliest occurrences of the expression hoop snake that I have found are as follows:

1-: From A Tour in the United States of America (London: Printed for G. Robinson, J. Robson and J. Sewell, 1784), by the Scottish travel writer John Ferdinand Smyth (1745-1814) [Vol. 1, Chapter 34, page 265]:

While I was at the Sawra Towns, one day a little lad of Mr. Bayley’s came to acquaint us that he had killed a horn snake, which being a curiosity that I was extremely desirous of observing and examining with particular attention, I accompanied him to the place where he said he had left it; but when we arrived there, to my great disappointment it was not to be found.
He assured me that it must not have been quite dead, and had recovered so much as to be able to crawl from the spot on which he had left it, and had secreted itself somewhere among the leaves.
However, every one, and all the inhabitants, with the greatest confidence asserted and avowed their having seen such snakes, though very seldom.
[…]
He is described as something resembling a black snake, but thicker, shorter, and of a colour more inclining to a dark brown. He never bites his adversary, but has a weapon in his tail, called his sting, of a hard, horny substance, in shape and appearance very much like to a cock’s spur: with this he strikes his antagonist, or whatever object he aims at, when he least expects it, and if it penetrates the skin, it is inevitable and sudden death.
[…]
As other serpents crawl upon their bellies, so can this; but he has another method of moving peculiar to his own species, which he always adopts when he is in eager pursuit of his prey; he throws himself into a circle, running rapidly round, advancing like a hoop, with his tail arising and pointing forward in the circle, by which he is always in the ready position of striking.
[…]
From the above circumstance, peculiar to themselves, they have also derived the appellation of hoop snakes.

2-: From Travels through the States of North America, and the Provinces of Upper and Lower Canada, during the years 1795, 1796, and 1797 (London: Printed for John Stockdale, 1799), by the Irish travel writer Isaac Weld (1774-1856) [Vol. 2, Letter 32, page 168]—the following is about the snakes found on the islands at the western end of Lake Erie:

Mr. Carver * tells of a serpent that is peculiar to these islands, called the hissing snake. […] Mr. Carver does not inform us of his having himself seen this snake; I am tempted, therefore, to imagine, that he has been imposed upon, and that the whole account he has given of it is fabulous. […] Were a traveller to believe all the stories respecting snakes that are current in the country, he must believe that there is such a snake as the whip snake, which, as it is said, pursues cattle through the woods and meadows, lashing them with its tail, till overcome with the fatigue of running they drop breathless to the ground, when it preys upon their flesh; he must also believe that there is such a snake as the hoop snake, which has the power of fixing its tail firmly in a certain cavity inside of its mouth, and then of rolling itself forward like a hoop or wheel with such wonderful velocity that neither man nor beast can possibly escape from its devouring jaws.

[* The reference is to Travels through the interior parts of North-America, in the years 1766, 1767, and 1768 (London: Printed for the author, 1778), by the American travel writer Jonathan Carver (1710-1780).]

3-: From the Rutland Herald (Rutland, Vermont, USA) of Saturday 24^th June 1809 [page 4, column 4]:

The Newton Gazette informs us of a Hoop-Snake, or as some call it a Horn-Snake, having been recently killed near that place—a reptile which is said to coil itself up like a hoop, and roll with such swiftness as to strike its horn a considerable distance even into a tree, which it is so poisonous as immediately to kill.

4-: From A Condensed Geography and History of the Western States, or the Mississippi Valley (Cincinnati: Published by E. H. Flint, 1828), by the American travel writer Timothy Flint (1780-1840) [Vol. 1, Ohio, page 363]:

The first travellers to explore Ohio availed themselves of the full extent of the traveller’s privilege in regard to the wonders of this new land of promise, and the unparalleled fertility of the soil. These extravagant representations of the grandeur of the vegetation, and the fertility of the land, at first excited a great desire to emigrate to this new and wonderful region. But some returned with different accounts in discouragement; and the hostilities of the savages were painted in the most appalling colors. A reaction took place in the public mind. The wags of the day exercised their wit, in circulating caricatured and exaggerated editions of the stories of the first adventurers, that there were springs of brandy, flax, that bore little pieces of cloth on the stems, enormous pumpkins and melons, and the like. Accounts the most horrible were added of hoop snakes of such deadly malignity, that a sting, which they bore in their tails, when it punctured the bark of a green tree, instantly caused its leaves to become sear, and the tree to die. Stories of Indian massacres and barbarities were related in all their horrors. The country was admitted to be fertile; but was pronounced excessively sickly, and poorly balancing by that advantage all these counterpoises of sickness, Indians, copper headed and hoop snakes, bears, wolves, and panthers.