Barron represented Ireland in the doubles competition at the 1996 Summer Olympics in Atlanta, partnering Owen Casey. The pair was eliminated in the first round there. The right-hander Barron represented Ireland in the Davis Cup from 1993–2001, posting an 11–11 record in singles and a 6–2 record in doubles in seventeen ties played. Barron's highest ranking in singles was World No. 263, which he reached on 19 March 2001. His highest doubles ranking was World No. 390, which he reached on 1 December 1997.