Barrett played hurling with the local Ballyduff team. He emigrated to London, joined a local hurling club and was selected for the London GAA team. He was a corner-forward on the London team which won the 1901 All-Ireland Championship, beating Cork GAA 1-5 to 0-4 in the final. It remains London's only senior All-Ireland hurling Championship title. Barrett also appeared for London in the final of the following year, but this time Cork gained revenge, thrashing London 3-13 to 0-0.
He won a gold medal as part of the City of London Police tug-of-war team in the 1908 Olympic Games in London. He also won a bronze medal in the heavyweight division of the freestyle wrestling competition.
Barrett also competed in the shot, javelin and discus competitions in the 1908 athletics programme, but wrestling was his premier sport. He was British heavyweight freestyle champion in 1909 and 1911. Barrett also competed in Greco-Roman wrestling in both 1908 and the Stockholm Olympics of 1912. He was defeated in the first round on both occasions.