It can be said of Supreme Court justices that most Americans would not know one when they saw one. This year, however, one made the cover of People magazine. Sandra Day O'Connor is stopped in public places and asked for autographs.

It can be said of oral argument at the Supreme Court that it is not one of the most popular shows in town. But this year, attendance by the public in the first two months of the term increased 30 percent.

The eight other justices seem socially invisible in this town. But there are so many requests for social commitments by O'Connor that she apparently does not have time to see fully what she is getting into.

O'Connor recently found herself contributing two autographed copies of the Declaration of Independence to what turned out to be a fund-raising auction for a legal defense fund. That is taboo for Supreme Court justices. A court spokesman said that being "flooded with requests, she was unaware" of the auction's purpose.

Nobody cares much about the comings and goings of, say, Justice Harry A. Blackmun. Nobody cared, for example, that Chief Justice Warren E. Burger rode a bicycle until an accident some years ago.

This year, there have been several inquiries about where O'Connor takes her exercise class, an item and cartoon in the American Bar Association journal about how she was asked for check-cashing identification at a local supermarket and a mention in the Ear gossip column about how she was spotted unloading personal belongings from a U-Haul rental truck at her new home.

That last item bothered her because it said where she lived. It attracted gawkers.

It is too early in her first term to say how O'Connor stands on the great issues of the time. But it is clear that the otherwise stuffy institution--the justices would call it something else, perhaps "dignified"--has been rendered a little less stuffy by her presence.

Clearly, she is not just another Supreme Court justice but, as Arizona Gov. Bruce Babbitt said last week, "a genuine American hero from right in our midst." Babbitt made the remark at "Sandra Day O'Connor Day," a home-state celebration for the first woman justice.

From her swearing-in, during which taking photographs was allowed for the first time in the Supreme Court conference room, to the flood of invitations she is receiving for public and private social events, no such fuss has ever been made over a new Supreme Court justice.

All of the hoopla may cease after O'Connor has been on the court a while. It is also conceivable that she enjoys the fuss, at least for now.

Reporters covering the court glimpsed her sociability the day she was sworn in.

Not invited to a major reception in her honor held in the grand entrance to the Supreme Court chamber that September day, the press held its own impromptu party in the cluttered basement press room. Assuming the gesture was futile, the press nevertheless invited O'Connor and her husband, John. They came.

The next few weeks were equally busy for her. There was the closing ceremony for Wolf Trap's 11th season. See the November issue of "Washington Dossier" magazine for pictures of the O'Connor's "swinging to the music" of the big-band sound.

There was a reception in her honor by the National Womens Political Caucus where she even gave a small speech--a rousing cheer for all women judges and lawyers. "I hope to see more of you out there" arguing before the court, she said.

There was the reception thrown last Sunday by the D.C. Bar, the reunion of Stanford graduates, the White House dinner for the king and queen of Jordan, the swearing-in of a new Washington Press Club president, and the upcoming dedication of a new YWCA headquarters.

The press club event led to the episode involving the auction. After the swearing-in, a member of Sigma Delta Chi, the Society of Professional Journalists, asked O'Connor to contribute something to a celebrity auction, according to Sigma Delta Chi officer Paula G. Wolfson.

Eventually, she sent over two copies of the Declaration of Independence, autographed by the first woman justice. The items fetched $240 three weeks ago at the auction.

Court spokesman Barrett McGurn said O'Connor did not know the money was destined for the society's legal defense fund. Like other such funds, it helps support court actions including Supreme Court actions favorable to journalists.

Judges are not supposed to involve themselves in that sort of venture or, for that matter, lend their names for any fund-raising effort.

That episode may illustrate why other justices keep their distance from the press and maintain such a low profile here. That way, they stay out of trouble.