Born at Orange Court House, Virginia, Jenkins entered the Navy as a midshipman on 1 November 1828, and served first in the West Indies in an expedition against pirates and slavers.

Prior to the Mexican–American War, Jenkins served with the United States Coast Survey and with the Brazilian and Mediterranean Squadrons.

In the interval between the wars, he served in the receiving ship at Baltimore, Maryland, returned to the U.S. Coast Survey, and was secretary of the Lighthouse Board.

After this, Jenkins became a captain and served primarily in the West Gulf Blockading Squadron of David Farragut, he commanded Oneida.

He was present at the Battle of Mobile Bay and heard Farragut utter the famous line "Damn the torpedoes, full speed ahead."