Leslie was born in Edinburgh. He played for Newtongrange Star in his youth. As a professional, he played for Scottish First Division sides Hibernian and Airdrieonians before playing in the Football League. In England, he played for West Ham United and Stoke City in the First Division, Millwall in the Second Division, and Southend United in the Fourth Division. He retired following the 1968–69 season. He also played for Scotland fives times in the early 1960s.