Norman played for numerous local junior teams in the 1920’s. After an unsuccessful trial with Manchester United in 1928, he joined Stockport as an amateur, swiftly moving on to Doncaster, non-league Crook Town, Bury, Swindon Town, and finally Belfast Distillery.
On 2nd November 1933, he signed for Dundee, and made his debut two days later against Motherwell. Quickly settling into the team, he was a favourite with the then manager, Billy McCandless, who along with the club directors, denied two transfer requests, first from Newcastle United and then Hull, in 1934.
Season 1938/39 got off to a slow start, it was not until he recovered from a cartilage operation that he regained his place in the team, becoming an almost ever present for the rest of that campaign. Before re-gaining full fitness, he had the opportunity to be a linesman at Den Park, in a match against Airdrie.
When football was shut down in the early stages of WW2, Norman was working at a foundry in Monifieth. By 1940 he had volunteered to join the R.A.F. He was one of the players that Dundee kept on their books throughout the war years, although he was allowed to turn out for Southport F.C., between 1941 and 1944, as a guest player. He played in the War Time League, the Football League War Cup, and other local competitions.
After getting his discharge papers in 1945, he returned to Dens Park, but by 1946 he was given the opportunity of a free transfer.
Like a lot of footballers, he was keen on other sports, and represented Forthill bowling club, played in the billiards league for Clepington, and cricket for Forthill C.C.