Born in East Victoria Park, Moriarty played under-12 and under-14 matches for Victoria Park in the local Temperance League, and progressed to the Victoria Park side in the Metropolitan Juniors Football Association in 1941, aged 16. He attended St. Patrick's Boys' School and Aquinas College, playing football for both schools. Falling into the Perth Football Club's recruitment zone, he made his senior debut for Perth in 1942 in the wartime age-restricted competition, and won the club's fairest and best trophy in his first season, playing mainly off a half-back flank. He also finished equal fourth in the 1942 Sandover Medal for the fairest and best player in the competition, with nine votes. In 1943, he won both his club's best and fairest and the Sandover Medal, finishing with 28 votes to become the first Perth player to win the award. Moriarty enlisted in the Army in September 1943, serving as a gunner in the 2nd Medium Regiment of the Royal Australian Artillery. He was posted to Sydney for training, and played seven games with the South Sydney Football Club in the Sydney Australian Rules Football League. He returned to Western Australia in time for the first game of the 1946 season, and was discharged from service in September 1946. He played with Perth on their tour of the Eastern states in July–August 1946, which included matches in Broken Hill, Wagga Wagga and Sydney. The game at Broken Hill attracted 5,000 spectators paying £389/15/9 where he was named in the best but did not kick a goal. Broken Hill won The game against Southern Riverina was played at the Rock before a crowd of 1750 which was a record for a mid-week game in the area. Perth won 18-25 to 14-4. The game against NSW was played at Trumper Park on 11 August and reportedly attracted a crowd in excess of 10,000 paying an amazing £464/14/6 at the gate after Perth won the game 22-15 to 18-16 Most often used as a half-back flanker, Moriarty played in two losing grand finals for Perth, in 1949 and 1950, before finally achieving a premiership in 1955, despite receiving a broken nose during the grand final. He finished his career in 1958 having played 253 games, which remains a club record. Towards the end of his career, he had been restricted by recurring hamstring injuries. Moriarty was inducted into the WestAustralian Football Hall of Fame in 2010, and died at Sir Charles Gairdner Hospital in Nedlands on 23 October 2011, after a short illness, with The West Australian noting he was "dour ball player with strong team values".