 A student at Glasgow's St Gerard's School, Craig was a Celtic supporter as a child, with the first game he attended being the Saint Mungo Cup final in 1951.He was a Scotland schoolboy international, while his first senior side was the University of Glasgow representative team which he played for while studying dentistry at the institution.He 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.