Domestically, Stoinis captained Melbourne Stars in the 2024–25 Big Bash League and has played Sheffield Shield cricket for Western Australia and Victoria.

[7] After playing several Futures League matches for the state under-23 side, Stoinis made his List A debut for Western Australia in the 2008–09 Ford Ranger Cup.

[12][13] He spent part of the 2012 English season playing for the Peterborough Town Cricket Club in the Northampton Premier League,[14] and in one match took a hat-trick.

[15] Stoinis also played five Second XI Championship matches for Kent County Cricket Club during his time in England.

[16] In December 2012, Stoinis was selected in the Perth Scorchers' squad for the 2012–13 Big Bash League season, replacing the injured Mitchell Marsh.

[25] In the Melbourne derby on 5 January 2020, Stoinis was fined $7,500 for a homophobic slur directed at Renegades bowler Kane Richardson.

[33] In March 2023, he was signed by the San Francisco Unicorns for the first edition of Major League Cricket in the United States.

[45] On 16 July 2020, Stoinis was named in a 26-man preliminary squad of players to begin training ahead of a possible tour to England following the COVID-19 pandemic.

[46][47] On 14 August 2020, Cricket Australia confirmed that the fixtures would be taking place, with Stoinis included in the touring party.