The contract to build Drum was awarded to Mare Island Naval Shipyard at Vallejo, California, on 15 March 1967, and her keel was laid down there on 20 August 1968. She was launched on 23 May 1970, sponsored by Mrs. William F. Bringle, wife of Vice Admiral William F. Bringle, commander of the United States Seventh Fleet, and commissioned on 15 April 1972 with Commander James L. Willis in command.