Adolphus Staton was born on 28 August 1879 in Tarboro, North Carolina. Appointed from that same state to the U.S. Naval Academy, he graduated in 1902 and reported for his two-year required sea duty on board USS Chicago and the newly commissioned cruiser Cleveland. Commissioned as an Ensign in May 1904, Staton tranferred to USS Connecticut, where he was promoted to Lieutenant in May 1907. After a tour on the gunboat Yorktown in June 1909, he became Officer in Charge of the Navy Recruiting Station at Los Angeles, California. Returning to sea duty in September 1911, he reported to USS Florida, transferring to the armored cruister North Carolina and later to USS South Carolina, where he participated in the intervention at Vera Cruz, Mexico. On 22 April 1914, Staton led his men with courage and skill to occupy the city. For his "distinguished conduct in battle" on this occasion, he was awarded the Medal of Honor. In June, he was ordered to Office of the Judge Advocate General in Washington, D.C. and was promoted to Lieutenant Commander in August 1905.
During World War I, Lieutenant Commander Staton briefly served on board USS Oklahoma before commanding USS Dubuque. In April 1918, after three months as Senior Naval Officer on board Army Transport Calamares, he served as Executive Officer on board the ex-German ship Mount Vernon. In July 1918, Staton was promoted to Commander. In February, he transferred to become the Executive Officer for the ex-German ship Leviathan. After fitting out the newly commissioned battleship Tennessee in June 1920, he became her Executive Officer. In April 1922, he graduated from the Naval War College at Newport, Rhode Island and returned as an assistant at the Judge Advocate General. In April 1924, he began a period of service commanding the ships USS Argonne, USS Asheville, and USS Black Hawk, where he was promoted in June 1925 to Captain. Returning to shore duty, he was in charge of the Officer's Discipline Division at the Bureau of Navigation in Washington, D.C.
In March 1929, Captain Staton became Commander, Destroyer Squadron Eleven, Battle Fleet, and transferred a year later to become Commander, Destroyer Squadron Six, Battle Fleet. After completing the Army War College course in Washington, D.C., he remained in the area and served under the Director of the Budget as Chief Coordinator. In July 1933, he became Assistant Director in the Office of Naval Intelligence with Naval Operations. In November, he commanded the battleship Nevada. In July 1935, he had staff duty with the Army School of Command at Fort Leavenworth, Kansas. In June 1937, Staton retired and was promoted to Rear Admiral on the retired list. In December 1941, he was recalled to active duty in the Office of the Under Secretary, administering laws to remove subversive radio operators from merchant ships. In June 1943, his post was terminated and he returned to inactive status. Adolphus Staton died on 4 June 1964 and is buried at Arlington National Cemetery, Arlington, Virginia.