He played junior hockey for the Regina Pats from 1969 to 1971. The Minnesota North Stars chose him 21st overall in the 1971 NHL Amateur Draft. Norrish turned pro in 1971-72 with the Cleveland Barons of the American Hockey League and only scored an assist in 39 games. The next season with the Barons he scored 22 goals and 33 assists. However he could not crack the North Stars lineup which was deep at left wing. He managed to get into 21 games over two seasons and scored 3 goals and 3 assists. He retired in 1975.