Of American-English origin, the expression tinfoil hat, also tinfoil cap, is used with allusion to the belief that such a hat or cap protects the wearer from mind control, surveillance or similar types of threat. Either extra-terrestrials or the government are frequently imagined to be the source of such threats.

This expression occurs, for example, in a letter from one Harold Tuchel, of Waterloo, about “loud, highly-partisan Republicans”, published in The Courier (Waterloo, Iowa, USA) of Sunday 4^th December 2022:

After two years of election denying and serial lying how can anyone trust such lying scoundrels? The real problem is partisans will refuse to believe a bi-partisan commission, and where would one find such fair people? After all, everything is a conspiracy. The FBI is conspiring against conservatives if you believe Republicans. Even the IRS is conspiring to enslave our citizens, according to Chuck Grassley ¹. Mr. Grassley needs a new tinfoil hat liner to make sure the IRS, FBI, CIA are not tuning into his thoughts.

¹ Chuck Grassley (born 1933) is a Republican Senator from Iowa.

The earliest occurrences of the expression tinfoil hat, also tinfoil cap, that I have found are as follows, in chronological order:

1-: From The Daily Olympian (Olympia, Washington, USA) of Monday 21^st August 1972:

Candle Sparks The Bender Home

Chunks of cardboard ignited by flames from a candle were blamed for the fire Monday morning which extensively damaged a one-story, wood-frame structure at 2428 East Beacon Street.
The occupant of the house, Stanley Bender, escaped unharmed.
Olympia Fire Department hosemen said the blaze broke out around 7:30 a.m. in a bedroom and quickly spread throughout the residence. Pumper trucks were on the scene for about 45 minutes before the flames finally were quenched.
Bender, who customarily wears a tinfoil-lined hat as protection for what he describes as bombardment from micro-waves, managed to salvage a water-soaked notebook from his burning domicile. He said the binder contains pages of drawings pertaining to his various inventions.

This photograph of Stanley Bender wearing a tinfoil-lined hat is from Candle Sparks The Bender Home, published in The Daily Olympian (Olympia, Washington, USA) of Monday 21^st August 1972:

STANLEY BENDER
He Saved Notebook

2-: From Skeptical Ufologist Says: If UFOs Are Real, At Least They’re Peaceful, by Tom Whitford, feature writer, published in the Daily Press (Newport News-Hampton, Virginia, USA) of Sunday 27^th February 1977—the following takes place in a café, where the author is meeting with Ron, a volunteer investigator for Aerial Phenomenon Research Organization, which studies UFO sightings:

As Ron lunched on a cheeseburger and French fries, no little green men popped up with their glassy-eyed stares and tinfoil caps to ward off dangerous rays. Not even a mention of being abducted or even ever seeing a UFO.

3-: From Phone calls home to Harrisburg reveal widespread confusion, by Richard Leiby, Times staff writer, published in The Tampa Times (Tampa, Florida, USA) of Saturday 31^st March 1979:
—Context: The author, who is from Camp Hill, near the Three Mile Island nuclear power station, where a major accident took place on Wednesday 28^th March 1979, is phoning his family and friends:

Kids still clowning

Of course, there’s always the apathetic voice of wanton youth to be heard. How, I wondered, was my Old Gang taking all of this?
“People are laughing at it,” said Mike Keller, 23, a certified Old Ganger who lives just down the road from my parents. Back in high school, Mike and I used to swim in the Susquehanna River near Goldsboro, in the shadow of the Three Mile Island cooling towers. We worried about snapping turtles then, not radiation.
Friday was Mike’s birthday. To celebrate, he and a few other friends were going to see “The China Syndrome”—the well-timed movie describing a nuclear disaster—just for kicks. Later, they hoped to hold a “Radiation Rock” party, “where you dress up in tinfoil hats to keep out the gamma rays or whatever they are.”

4-: From The Calgary Herald (Calgary, Alberta, Canada) of Thursday 13^th September 1979:

Fans, foes and wierdos [sic] write the mayor
Dear Mr. Mayor: Please fix taps, zaps

By Don Martin
(Herald staff writer)
A nasty neighbor’s deadly rays were bombarding his house and the tin foil cap on his head was not adequate protection from being “zapped.”
So the man wrote Mayor Ross Alger ² for help.
Another fellow, who kept hearing a voice in his water tap, wrote Alger to “get off your butt and stop it.”
It goes with the job—the chains of office attract mail from fans, foes and weirdos alike, meaning Alger is usually swamped with letters from the citizens of Calgary.

² Ross Alger (1920-1992) was the Mayor of Calgary, Alberta, Canada, from October 1977 to October 1980.

5-: From Police dispatchers are the unheralded angels, by George E. Jordan, published in The Plain Dealer (Cleveland, Ohio, USA) of Sunday 16^th May 1982:

In a 9^th-floor office at Cleveland police headquarters, 77 women and men work in a job seldom heralded and often invisible—until someone makes a mistake.
These civilian dispatchers answer as many as 400 telephone calls an hour from those seeking help, advice or simply the sound of another’s voice. […]
[…]
Another dispatcher, 26, had a lighter tale:
A Cleveland woman telephoned last year to complain that her neighbor was shooting an invisible death ray at her. She wanted the police to stop it.
The dispatcher suggested she wear a tin foil hat and put tin on her windows to deflect the rays.
“The woman called a few weeks later and wanted to know whether you put the shiny side out or in,” he said. “A zone car went by her house real slow one day and saw this woman working in her yard with an aluminium hat on. After she did it, she was happy.”

6-: From the review of Lovesick (1983), a U.S. romantic-comedy film written and directed by Marshall Brickman, and starring Dudley Moore and Elizabeth McGovern—review by Bill Cosford, Herald film critic, published in The Miami Herald (Miami, Florida, USA) of Saturday 19^th February 1983:

Along the way, a marriage is smashed, a suicidal patient is abandoned, and a derelict is turned out into the street, wearing a tin-foil hat to keep the Trade-Center beams off his brain.

7-: From A microwave maelstrom inspires new tinfoil decor, by Diana McClellan, published in The Sun (Baltimore, Maryland, USA) of Thursday 8^th September 1983:

ALL MY CHILDREN SEARCH FOR THE YOUNG AND THE RESTLESS . . . Tense times at the dear old Corporation for Public Broadcasting. As you know, darlings, the CPB headquarters here nestles cheek-to-cheek with Aeroflot and the Soviet Embassy—whose rooftop bristles with busy antennae—and the Washington Post, where rooftop satellite saucers constantly suck Truth from the Cosmos. Worried stiff about the effect of all those microwaves on his sex life and his synapses, one CPB biggie has carefully lined his entire office with tinfoil. Just in time, too. Another biggie there toured the building the other afternoon to monitor CPB’s high-toned shows in his underlings’ offices. Darlings: Every single tube in the joint was tuned to a Soapie. Now, there is talk of passing out tinfoil hats to the staff. A wonderful idea. Ear has been wearing one for years.