George Michael's new single, ''I Want Your Sex,'' has become the first record to run into censorship problems because of fears that it might be too sexually explicit for the age of AIDS.

The song, which is featured on the soundtrack of the movie ''Beverly Hills Cop II,'' has been banned from daytime play in Britain by the BBC's Radio One. In the United States, many radio stations have refused to play the record, at least temporarily.

Only one of the New York area's two leading Top-40 radio stations, WHTZ, is playing the record. The other station, WPLJ, has taken a more cautious attitude. A spokesman for Columbia Records, Marc Benesch, said yesterday that stations in Pittsburgh, New Orleans, Cincinnati, Minneapolis and Denver were also not playing the record because of concern over its lyric content. These objections, however, did not keep the record from getting off to a fast start, entering Billboard's Hot 100 chart this week at No. 51.

Columbia is releasing the single in three versions: 7-inch, 12-inch and compact disk formats.

''I Want Your Sex'' is a Latin-flavored funk song whose lyric reads in part:

''I've waited so long, baby Out in the cold I can't take much more, girl I'm losing control I want your sex I want your love I want your sex It's natural It's chemical it's logical, Habitual, it's sensual But most of all sex is something we should do.''