He made his first-class debut for Derbyshire in the 1880 season against a team of touring Australians, in which he scored a duck in his first innings but became the top scorer for the team in the second, making 24 before he was run out.
Barrington played his debut County match three days later against Lancashire, in which he made 24 again and 20.
Barrington only played one County match between the end of 1881 and the beginning of 1884, though when he returned for the team, in the first game of the 1884 season, his first game, against Sussex, included his first and only half-century of his career, once again batting in the opening order.
Barrington was a right-handed batsman and played 48 innings in 25 first-class matches with an average of 9.68 and a top score of 50.
He was a round-arm slow bowler and took 1 first-class wicket for 27 runs.