Born in Penrith, New South Wales, Cartwright played his junior football for St Mary's Saints before being signed by the Penrith Panthers. Cartwright attended Patrician Brothers' College, Blacktown.
From 2012 to 2014, Cartwright played for the Penrith Panthers' NYC team.
In April 2013, Cartwright re-signed with the Panthers on a 2-year contract.
At the end of 2013, Cartwright was named at second-row in the 2013 NYC Team of the Year, won the 2013 NYC Player of the Year award, played in the Panthers' 2013 NYC Grand Final win over the New Zealand Warriors and played for the Junior Kangaroos.
In Round 12 of the 2014 NRL season, Cartwright made his NRL debut for the Panthers against the Parramatta Eels off the bench in the Panthers 38-12 win at Penrith Stadium. In Round 19 against the Sydney Roosters at SFS, Cartwright scored his first NRL career try in the Panthers 32-12 loss. In Round 21 against the Canterbury-Bankstown Bulldogs, Cartwright suffered a season ending ankle injury in the Panthers' 22-16 win at ANZ Stadium. Cartwright finished his debut year in the NRL with him playing in 7 matches and scoring a try for the Panthers in the 2014 season. On 9 September 2014, Cartwright extended his contract with the Panthers from the end of 2015 to the end of 2018.
Cartwright finished off the 2015 season having played in 22 matches and scoring 5 tries for the Panthers.
In February 2016, Cartwright was named in the Panthers 2016 NRL Auckland Nines squad. In Round 5, Cartwright scored the winning try on the final siren against the Parramatta Eels at Parramatta Stadium giving the Panthers the 20-18 victory. On 8 May 2016, Cartwright played for New South Wales City against New South Wales Country where he started at second-row in the 44-30 win in Tamworth. Cartwright’s good form during the season saw him selected in the New South Wales Blues training squad but did not make his expected origin debut. In mid-way during the season, after the Panthers released seasoned five-eighth Jamie Soward to England and a long extended shoulder injury to rookie half Te Maire Martin, Cartwright stepped up from second-row to make his the five-eighth position as his own alongside boom rookie halfback Nathan Cleary, playing some exciting footy as a young halves combo to lead the Panthers into a late season finals charge. On 22 September 2016, Cartwright extended his contact with Panthers to the end of the 2021 season. Cartwright finished an enjoyable 2016 NRL season with him playing in all of the Panthers 26 matches, scoring 8 tries and kicking 1 goal. In December 2016, Cartwright was caught up in an ugly situation involving his ex-girlfriend where she uploaded pornographic images of him in Revenge porn attack and threatened to kill him in a drunken Facebook rant video.
On 10 February 2017, Cartwright played in the 2017 All Stars match for the World All Stars against the Indigenous All Stars where he started at second-row in the 34-8 loss at Hunter Stadium. In March 2017, more allegations about Cartwright were circling around, his ex-girlfriend known as Miss X claiming that Cartwright and Panthers club intermediary Lew Zivanovic played her $50,000 to get an abortion, after he left her when she fell pregnant to him. Zivanovic later claimed that Miss X wanted an extra $200,000 in cash on top of an alleged wishlist, including reimbursement for two overseas post-abortion holidays worth $176,000, but she strong denies these claims.
Cartwright is the nephew of former Penrith Panthers and Salford player and former Gold Coast Titans coach, John Cartwright.