[2] In June 2018, Kirton was selected to play for the Montreal Tigers in the players' draft for the inaugural edition of the Global T20 Canada tournament.
[7][8] Kirton made his List A debut for Canada in the 2018 ICC World Cricket League Division Two tournament on 8 February 2018.
[9] In October 2019, he was named in Canada's squad for the 2019 ICC T20 World Cup Qualifier tournament in the United Arab Emirates.
[11] In March 2023, he was named in Canada's squad for the 2023 Cricket World Cup Qualifier Play-off.
[12] He made his One Day International (ODI) debut on 27 March 2023, for Canada, against Jersey in that tournament.