Dorow, a quarterback, played college football at Michigan State University and was All-American in 1951.

After serving the required two years in the military, Dorow played for the Washington Redskins during the 1954, 1955, and 1956 seasons, and for the Philadelphia Eagles in 1957.

After being released by the Eagles before the start of the 1958 season, Dorow spent two years in the Canadian Football League, playing for Saskatchewan, British Columbia, and Toronto.

Dorow injured his arm in the fourth game of the 1962 season and was unable to play again.

After leaving professional football, Dorow was a backfield coach for Hillsdale College in Michigan for the 1963 and 1964 seasons.