Brian Clarke was placed under house arrest by Israelis in the Washington Hilton, told to cool his heels with servants in the Egyptian Embassy and teased yesterday by President Carter. But he got what he wanted.

Clarke, who described himself as "a lonely political science major," strode from the White House Oval Office yesterday with a document bearing the hard-won autographs of Israeli Prime Minister Menachem Begin, Egyptian President Anwar Sadat and Carter.

The document was a mimeographed White House copy of a Carter speech Sept. 18 to a joint session of Congress that came after the Camp David accords on peace in the Middle East.

Clarke, 20, an aid to Rep. Henry S. Reuss (D-Wis.), said he already has been offered $1,000 for the document. But he wants to hold off, he said, and perhaps sell the paper to send his children to college.

It wasn't easy getting "those guys" to sign the speech, Clarke said.

His quest began after Clarke heard Carter tell Congress that "the summit exceeded our expectations." Rosalynn Carter was moved to tears by the speech and Clarke came up with the idea of getting the three autographs.

The next morning, Clarke said, he went to the White House, picked up a copy of the speech and took off for the Washington Hilton where Begin and his entourage had taken over the hotel.

"I had to wait for five hours. They put me in a room, said I was under house arrest and that they were going to check me out," Clarke said.

Checked out and cleared, Clarke said an Israeli press aide led him into a crowded room where Begin was sitting. "He shook my hand, signed the speech and mumbled something about this was an excellent idea," Clarke said.

Clarke then drove to the Egyptian Embassy on Massachusetts Avenue and waited in the press room at the embassy from 5 p.m. to 11:30, when he was asked to wait at the servants' entrance for another hour, he said.

"Around 2 a.m. I got into the room where Sadat was... Sadat shook my hand and looked at Begin's signature.

"Sadat said, 'My friend (Begin) wrote small, so I will write small and the great one (Carter) will sign large,'" Clarke said.

The next morning Clarke called the White House to see if "the great one" would sign the speech. "They said no right off. That kind of ticked me off because these other guys signed it and my own president wouldn't," said Clarke who lives in McLean. So he started pestering the White House. "They weren't terribly nice and I was a bit of a pain."

Wednesday, after two months of pestering, Clarke got a call telling him he had appointment with the president at 12:10 p.m. the next day.

"I was scared as a chicken. The staff people tried to calm me down. Then I met President Carter and explained how I got everyone else to sign," Clarke said.

The president smiled, Clarke said, and asked, "What would you do if I didn't sign it?"

"I said I would be very upset," Clarke said, "and he signed it."