"Elliot" got underway on 24 January 1977 for her maiden voyage, transiting from Pascagoula, Mississippi, to San Diego, California, via the Panama Canal. She was assigned to the U.S. Pacific Fleet as a unit of Destroyer Squadron 9 (DesRon 9), under the administrative control of Commander, Cruiser Destroyer Group Five and Commander, Naval Surface Forces Pacific. After arrival, "Elliot" conducted five weeks of shakedown training and participated in a combat exercise. Following these evolutions, she returned to her builders for a post shakedown yard availability.