Norman McCaw began his career with a three-year spell with Combination side, Park End. He then had a brief spell with Glenavon before teaming up with his brother, full Irish international Harold McCaw, at Linfield in 1928. Norman played mainly reserve-team football while at Windsor Park and moved on to Broadway United for the 1929-30 season. With Broadway he was part of the team that defeated Linfield Rangers 5-0 in the Steel & Sons Cup Final.
In 1930 McCaw moved on to Cliftonville, where he was to spend the lengthiest spell of his career. He was a regular for Ireland Amateurs during his spell at Solitude, winning nine caps and scoring twice between September 1930 and April 1936. The second of those goals put Ireland 4-1 up against England before the Irish had to fight-off a spirited comeback to hold on for a 4-3 win.
The all-amateur Cliftonville seldom challenged for the major honours, but in 1934 they did qualify for the Irish Cup Final, defeating Derry City and Glentoran along the way, only to lose out 5-0 to Linfield in the Final at The Oval. McCaw was praised for his craft, speed and dangerous left-foot reminiscent of his more decorated brother’s. However, he lacked his sibling’s robust style and energy.
McCaw’s tally of 35 goals for Cliftonville in the 1931-32 season remained a club record until surpassed by Liam Boyce in 2013 and his 115 career total for the Reds leaves him fifh on the club’s all-time list as of 2016.