Born in Scone, Graham was scouted as a kid by local club St Johnstone and spent several years there before leaving after having issues with coaches, and later joining Dundee's youth setup.

[9] Graham would score his first goal for the club in his 2nd appearance, in a league win over Bonnyrigg Rose Athletic.

[13] Graham scored his first goal for the Gable Endies on 4 November 2023, in a big league win away to Edinburgh City.

[17][18] Graham made his competitive debut for the Dark Blues on 23 July as substitute in a Scottish League Cup group stage win over Annan Athletic.

[21] On 20 September 2024, Graham joined Scottish Championship club Falkirk on loan until the end of the season.