WASHINGTON (AP) _ Cpl. Lindsey Scott, the Marine whose conviction on rape, kidnapping and attempted murder charges was overturned this summer, will face a new court- martial on Jan. 25, the Marine Corps said Friday.

Scott, who was released from prison in July after a successful appeal to the U.S. Court of Military Appeals, was informed in October the Marine Corps intended to present his case to a new court-martial. At the time, however, no date was set for the new proceeding.

Scott's Oct. 30, 1983, conviction was reversed by the nation's highest military court on July 6 on grounds the defense mounted by his civilian attorney during the first trial fell ''far short of reasonable competence.''

The court concluded Scott's civilian attorney had improperly failed to investigate the Marine's alibi.

Scott, then 25, was convicted of abduction, rape, sodomy and the attempted murder of the wife of a fellow Marine while posted to Quantico. The attack occurred on the evening of April 20, 1983.

Scott provided an alibi, asserting he was out shopping at the time and had been seen by various witnesses in the stores.

Following his conviction, Scott was sentenced to 30 years at hard labor, the forfeiture of $18,000 in salary, reduction to the rank of private and a dishonorable discharge.