[2] Graham played his junior rugby league for Blacktown City and attended The Hills Sports High School before being signed by the Penrith Panthers.

Graham was invited to represent the Portugal national rugby league team in the 2012 Cabramatta International Nines tournament.

[14] In Round 17 against the Wests Tigers, Graham played his 100th NRL career match, scoring a try in Cronulla's 36–22 win at Remondis Stadium.

[17][18] On 22 August 2014, Graham became one of the Cronulla players to accept reduced bans from the Australian Sports Anti-Doping Authority for his role in the 2011 Sharks supplements scandal.

[21][22] He co-captained the Sharks alongside Michael Ennis for a period whilst Cronulla's regular captain Paul Gallen was sidelined due to injury.

[citation needed] On 2 October, Graham was part of the Cronulla side that won the 2016 grand final to claim the club's first ever premiership.

[27][28] In 2018, Graham was not selected for NSW by coach Brad Fittler for the 2018 State of Origin series due to being out with injury for most of the first half of the 2018 season.

[29] In week one of the 2018 NRL finals, Graham was taken from the field in the first half during Cronulla's match against Eastern Suburbs with subsequent scans revealing the player had torn his anterior cruciate ligament (ACL) ruling him out for the rest of the season.

[31] Graham was selected for Game 2 of the 2019 State of Origin series where he starred in New South Wales' 38–6 win at Perth Stadium.

[citation needed] Graham played 19 games for Cronulla in the 2020 NRL season as the club finished 8th and qualified for the finals.

[38] Graham decided to end his season prematurely due to three head concussions he sustained including two in consecutive weeks.

[39] Graham played a total of 18 games for Cronulla in the 2022 NRL season as the club finished second on the table and qualified for the finals.