Dorow, a quarterback, played college football at Michigan State University and was All-American in 1951. He was drafted in the third round of the 1952 NFL Draft. 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 moved to the AFL for its inaugural season, playing for the New York Titans (forerunner of the New York Jets) in 1960 and 1961, before being traded to the Buffalo Bills for the 1962 season. Dorow injured his arm in the fourth game of the 1962 season and was unable to play again.
Dorow's awards include All American in football for MSU in 1951. Dorow's other accomplishments include leading the AFL in most touchdowns thrown (26) in 1960. Dorow also co-holds the CFL single-game record for sacks with 7, matched by two others.