Mr. Sinatra saw the file well before his death on May 14 at the age of 82. He had requested it under the Freedom of Information Act in 1979 and 1980. It was released today to journalists and others who had requested it.

The rumor concerning Mr. Sinatra and the draft led the F.B.I. to gather information concerning his arrest in 1938 on sex charges.

One F.B.I. report said that independent of the draft rumor investigation it had come to the bureau's attention that Mr. Sinatra had a criminal record in New Jersey. From the Bergen County Jail in Hackensack, ''there was obtained an enclosed picture of Frank Sinatra and the following information regarding the two occasions on which Sinatra was held in the Bergen County Jail,'' the report said.

The report read: ''FRANK SINATRA, Arrest #42799, Bergen County Sheriff's Office, Hackensack, New Jersey was arrested on November 26, 1938 charged with Seduction. Disposition was marked, 'Dismissed.' FRANK SINATRA, Arrest #42977, was arrested on December 22, 1938, charged with Adultery.''

Neither of the acts with which Mr. Sinatra was charged is against the law today, but his initial charge in 1938 stated that ''on the second and ninth days of November 1938 at the Borough of Lodi'' and ''under the promise of marriage'' Mr. Sinatra ''did then and there have sexual intercourse with the said complainant, who was then and there a single female of good repute.''

This, the charge stated, was ''contrary and in violation of the revised statute of 1937.''

The report noted that Mr. Sinatra was released on $1,500 bond and that the complaint was withdrawn when it was determined that the woman involved was married. A complaint of adultery was substituted, with Mr. Sinatra's bond being lowered to $500. That charge, too, was dismissed.

Other parts of the F.B.I. file concern Mr. Sinatra's links to mobsters. In one report he is mentioned with his old friend Jilly Rizzo, as well as criminals like Aniello Dellacroce, Carlo Gambino, Joe Gallo and Anthony Carillo, in connection with a case involving an effort to extort $100,000 from a New York stockbroker.