Shaw was developed by Oaks Fold (a Sheffield United nursery club in the 1950s), after having played for Sheffield Schoolboys, chiefly at half-back. He signed professional forms for United when he was 17. A calm stylish player, who had pace and tackled well, he could place his clearances.
Shaw went on to become an England International and made 5 appearances for the national side. His first cap was against U.S.S.R. at Wembley on 22 October 1958. It was a match England won 5-0. He went on to make 4 more appearances for England between 1958 and 1962.
In 1967, Shaw left United and joined Doncaster Rovers making 22 appearances for the Rovers.