Barton was born in Warren, Rhode Island on May 26, 1748. He worked as a hatter in Providence, Rhode Island. In 1771, he married Rhoda Carver. In 1775, he enlisted in the Continental Army as a corporal. He fought in the Battle of Bunker Hill. On August 2, 1775 he was appointed the adjutant of Richmond's Rhode Island Regiment. He was promoted to captain on November 1, 1775. In 1783 Barton became an original member of the Rhode Island Society of the Cincinnati. When Rhode Island ratified the Constitution of the United States in 1790, Barton was sent to New York to notify George Washington.