Sen. Arlen Specter (R-Pa.), a member of the Senate Judiciary Committee, has asked for the appointment of an independent counsel to investigate allegations of cocaine use by a longtime aide to Attorney General Dick Thornburgh, a spokesman for the senator said yesterday.

The senator's request underscored the growing political sensitivity of a federal inquiry into cocaine use among present and former public officials in Pennsylvania. Among the principal targets is Henry G. Barr, 47, an ex-federal and state prosecutor who served as Thornburgh's general counsel when he was governor of Pennsylvania and later as his special assistant in the Justice Department charged with overseeing and coordinating criminal investigations, including drug cases.

Thornburgh, four of his top staff aides, and Jim West, the acting U.S. attorney in Harrisburg have all recused themselves from the case because of their longtime associations with Barr, who resigned from the Justice Department in May 1989. But Specter, in a letter last week to Deputy Attorney General William Barr (no relation), said that as a result of recent developments in the case, "it is my conclusion that an independent counsel should be appointed in the matter involving Mr. Henry Barr."

William Barr said he had not yet seen the letter. Federal law calls for the department to investigate whether an independent counsel is needed if it receives information from a "credible" source that a criminal act has been committed by a senior administration official or someone who has served in that position in the past three years.

Specter's letter follows the recent disclosure of court briefs filed by the lawyer for another key figure in the case, former top Pennsylvania prosecutor Richard L. Guida, stating that Guida and at least four other witnesses have told a federal grand jury that they witnessed Barr use cocaine or accept delivery of it on repeated occasions between 1985 and sometime in 1988.