Born in Charleston, South Carolina, Drayton was the son of a prominent lawyer William Drayton who eventually relocated to Philadelphia, Pennsylvania. The family property in South Carolina, Magnolia Plantation, still owned by the Draytons, is a modern tourist attraction.
Drayton was appointed a Midshipman in the Navy in December 1827 and initially served in the south Atlantic on board the frigate Hudson. He attained the rank of Lieutenant in February 1838 and had assignments in the Mediterranean, Pacific, and Atlantic, as well as shore duty at the Naval Observatory in Washington, D.C., and at the New York Navy Yard. Promoted to Commander in September 1855, Drayton subsequently served as a staff officer during the Paraguay Expedition. At the beginning of the Civil War in 1861 he was stationed at the Philadelphia Navy Yard, where he helped prepare ships for war service.
In the fall of 1861 Commander Drayton was placed in command of the gunboat Pocahontas, in which he participated in the capture of Port Royal, South Carolina. His brother Thomas F. Drayton, a graduate of West Point and classmate of Jefferson Davis, was a general of the Confederate army and commanded the forts destroyed in this engagement.
Percival Drayton became commanding officer of the sloop of war Pawnee and was active in inshore operations in the waters of South Carolina, Georgia and northern Florida through the summer of 1862. He was promoted to Captain in July of that year. In September 1862, he was given command of the ironclad Passaic, overseeing her outfitting and working with John Ericsson to improve elements of monitor design. Drayton commanded his ship in attacks on Forts McAllister and Sumter in March and April 1863, experiences that reinforced his opinion concerning the limitations of the monitor type when fighting against well-defended fortifications.
Captain Drayton's next assignment was as Superintendent of Ordnance at the New York Navy Yard. In December 1863 he began a year as Fleet Captain to the commander of the West Gulf Blockading Squadron, Rear Admiral David Glasgow Farragut. Also commanding the squadron flagship, the big sloop of war Hartford, he took part in the August 1864 Battle of Mobile Bay and the following operations within Mobile Bay. Appointed Chief of the Bureau of Navigation in late April 1865, Drayton was taken sick and died at Washington, D.C., on 4 August 1865.