The U.S. District Court, acting on a recommendation by Attorney General William French Smith, appointed a 35-year-old career employe with the Federal Bureau of Prisons yesterday to run the troubled U.S. Marshals Service in the District of Columbia.

Robert L. Matthews, most recently warden of a federal prison in Ashland, Ky., was sworn in yesterday by Chief Judge Aubrey E. Robinson Jr. He will head a 106-member service, the largest in the country.

Matthews succeeds Anthony J. Furka, who held the post for six months on an interim basis after U.S. Marshal James O. Golden was fired last August.

Golden, who served just two weeks on the job, was fired after a series of sharp management disputes with his superiors at the service's national headquarters in Virginia. One of the disputes centered on who would take presidential assailant John W. Hinckley Jr. from St. Elizabeths Hospital, where he is confined, to a court hearing.

In addition to the turmoil caused by Golden's firing, a federal grand jury is investigating a small number of deputies for allegedly taking bribes from eviction companies to help those companies carry out court-ordered evictions. One deputy pleaded guilty last month to bribery charges.

Associate Attorney General Rudolph W. Giuliani said in a statement yesterday that the department recommended Matthews because of his "demonstrated management abilities" in several positions at the Bureau of Prisons