Barron is the son of James Pressley Barron (1920—2006), a World War II U.S. Army veteran and an analyst for the Central Intelligence Agency who received the Intelligence Commendation medal upon his retirement in 1985, and Leirona T. Barron, a former assistant principal of Thomas Jefferson Junior High School in Arlington, Va.
Barron is married to Dr. Jane-Iris Farhi, a cardiologist.