Craig joined Celtic in 1963, on amateur terms, so as to allow him to complete his studies and having done so, signed as a full professional in January 1965.
Craig’s abilities and style of play matched manager Jock Stein’s tactical philosophy and he soon displaced Willie O’Neill and Ian Young as Celtic’s regular right back. Stein encouraged his fullbacks to overlap the side’s midfield to provide additional support to the forwards, in the style of the modern wing-back role, and in Craig and left back Tommy Gemmell he found willing protagonists.
During his tenure at Parkhead, Craig collected 14 domestic honours as well as a European Cup medal in 1967. He made 231 appearances for Celtic scoring 6 goals. He won one cap for the Scotland national side.