In 1960 he was selected to play his first game for the state, which meant travelling to Western Australia. In order for him to be allowed to travel out of the state, the South Australian Soccer Federation had to get permission from the Protector of Aborigines (Clarence Edmund Bartlett, who also wrote a book about Point McLeay mission). Also in 1960, Moriarty was the first recognised Indigenous Australian to be selected for a national soccer team. He was selected to play in an Australian national team tour to Hong Kong, but the tour was cancelled after Australia's expulsion from FIFA.