NASA announced yesterday that Sen. Jake Garn (R-Utah) has accepted its invitation to take a ride on the space shuttle, possibly preempting White House intentions to have a teacher make the first citizen flight.

Garn, 52, has more hours as a pilot than all but one of the current astronauts and has sought openly the first congressional space junket.

As chairman of the Senate Appropriations subcommittee that oversees the National Aeronautics and Space Administration's budget, his support is critical to the agency's hopes to put an $8 billion space station in Earth orbit in 1992. In August, during the just-concluded election campaign, President Reagan ordered NASA to carry an elementary or secondary schoolteacher into orbit aboard the shuttle as the nation's first citizen space passenger.

Until now, space crew members have been astronauts, scientists or mission specialists trained for specific tasks such as operating the shuttle's robot arm.

It is not clear, NASA said yesterday, whether Garn will reach space before a teacher because neither has been scheduled on a specific flight.

Garn told reporters in Salt Lake City yesterday that he hopes to be on the shuttle Challenger's scheduled flight Feb. 12, when the Senate will be in recess. NASA sources said Garn could go no earlier than May.

Garn's prospective shuttle ride extends to space a longtime senatorial perquisite to try out the new technology that the taxpayers buy. Sen. Barry Goldwater (R-Ariz.), a pilot and one of the Air Force's strong advocates, has flown many advanced airplanes. Retiring Sen. John G. Tower (R-Tex.) visited Fort Hood, Tex., to take a close look at the controversial and sometimes dysfunctional M1 tank.

"This is not different than our oversight capacity, except it is a little different being in space," Garn told reporters in Salt Lake City yesterday. He said his wife had not yet been told about the flight, for which he applied four years ago.

"She preferred I not go but if something happens to me, she knows I'd die with a smile on my face," Garn said.

Garn said he has been keeping in shape for the flight by running 20 to 25 miles a week.

NASA officials said the invitation to Garn was worked out between Garn and NASA Administrator James M. Beggs and did not involve the White House.

In a hand-delivered letter, Beggs on Tuesday invited Garn to be a shuttle passenger "to make an inspection tour and flight aboard the shuttle given your NASA oversight responsibilities."

Sheila Griffin of NASA's press office said that other members of Congress have not been invited, but that "any chairman of committees directly responsible for NASA activities would be considered if they are interested."

Rep. Edward P. Boland (D-Mass.), chairman of the House Appropriations subcommittee in charge of NASA's budget, said through a spokesman that he, too, is interested in making a shuttle flight.

NASA is planning shuttle flights on at least a monthly schedule beginning next year, Beggs' letter said. On the May flight, a crew of five is to deploy three communications satellites from the space shuttle Columbia. Garn will need about six weeks of training with the crew before the flight, NASA said.

There have long been rumors that Garn would be the first member of Congress in space, but his office and NASA have denied them. At least twice, NASA spokesmen laughed at the suggestion and said there was no truth to it.

NASA noted that Garn is a colonel in the Air Force Reserve with more than 10,000 flying hours, a total only one current astronaut, Joe Engle, exceeds. Garn was a Navy fighter pilot during the Korean War.

A Utah firm, Morton-Thiokol Corp., has had $1.548 billion in NASA contracts since 1973, the year before Garn was elected to the Senate. It builds the solid rocket motors that help drive the space shuttle into orbit.

Teacher groups suggested after Reagan's campaign pledge to put a teacher in space that there were other, more pressing needs in education. But many teachers were pleased at the idea.

"I guess it's the first campaign promise that's been broken, but today's not the day to get too worked up about that," Bella Rosenberg of the American Federation of Teachers quipped yesterday.

Howard Carroll of the National Education Association, the other big teachers' union, said, "I don't know if we'd want to comment on Garn going up. The election's over. We just got the hell kicked out of us; we're in kind of a let's-bring-the-country-together mode today."