Moran threw and batted right-handed, stood 5 feet 11 inches (1.80 m) tall and weighed 185 pounds (84 kg).

Moran's professional career began in 1952 in the Cleveland farm system, and he missed the full seasons of 1955–56 while performing military service.

Moran started in both All-Star games that season, collecting two hits in seven at bats and playing errorless ball in the field.

Meanwhile, the Angels stunned baseball by finishing third in the American League standings in the team's second season of existence.

The following season, Moran lost his job to rookie Bobby Knoop and in June he was sent back to the Indians in a three-team trade also involving the Minnesota Twins, and finished his MLB career as a utility infielder with Cleveland in 1964–65.