He was a prodiguous try scorer and played in South Sydney's three Premiership victories between 1953 and 1955. In 1953 he scored three tries in the 31–12 Grand Final against St George, capping off a season where he was Souths leading try scorer with a tally of 23. This total stands in 3rd place in the club's all-time list of most tries in a season. He debuted for Australia in the inaugural World Cup in France in 1954. Moir also played Tests against all the rugby league playing nations and toured Great Britain with the 1956 Kangaroos where he played in two Tests and 14 tour matches and topped the tour try scoring list with 13 tries. He also featured in Australia's victorious 1957 World Cup campaign played at home. Said to have been the fastest winger in the Sydney competition, he is one of six Rabbitohs players to score five tries in a match, doing so in Round 7 of 1957 against Parramatta at Redfern Oval. His 105 career tries for the Rabbitohs in 110 games stands in 2nd place behind Benny Wearing's 144 in the all-time club record list.
In 2004 he was named by Souths in their South Sydney Dream Team, consisting of 17 players and a coach representing the club from 1908 through to 2004.