After a junior career with the Kingston Collegiate Institute of the Ontario Hockey Association, Stewart starred in senior hockey for several teams in the OHA from 1914 to 1924, most notably for the Toronto Dentals for four seasons while undergoing medical training, being named to the league's Second All-Star Team in 1918 and the First All-Star Team in 1919. He also won the Allan Cup with the team in 1917. With the Hamilton Tigers' senior team in 1922, 1923 and 1924, Stewart was named the First Team All-Star goaltender all three seasons.
The Boston Bruins began play in 1924 and losing eight of their first nine games, often by wide margins, and desperate for goaltending, signed Stewart to a contract. He played the rest of the schedule for Boston, winning five out of twenty-one games for the weak club, adding two shutouts. He remained the Bruins' goaltender for two more seasons, his best record coming in 1926, when he had a 16-14-4 record with six shutouts and a 2.21 goals against average.
Stewart finished his NHL career with a 30-41-5 record and ten shutouts in 77 games, recording a 2.45 goals against average.