[4] Curtis played his junior rugby league for the Bundeena Bushrangers and Cronulla-Caringbah JRLFC, before being signed by the Cronulla-Sutherland Sharks.
[6] In September 2015, he signed a three-year contract with the Melbourne Storm starting in 2016, beating 11 rival NRL clubs to his signature.
[10] In October, Scott was part of the Melbourne Storm's premiership winning team against the North Queensland Cowboys in the 2017 NRL Grand Final.
[13] On 7 October, Scott earned his first representative jersey as he was named in the Australian side for the 2019 Rugby League World Cup 9s.
[15] He missed large chunks of the 2020 season due to both indifferent form and injury, with his 2020 campaign ultimately ending when he hurt his right leg against Canterbury-Bankstown in round 16.
The Canberra side released a statement saying "The board decided that Curtis Scott's prior behaviour and recent assault charge has brought the club into disrepute, and they could not ignore this and the responsibilities that his NRL playing contract entails.
"The board said the club would continue to support Curtis Scott's ongoing rehabilitation and it will be in contact with NRL Welfare in this regard".
It was alleged that Scott had thrown a mobile phone at a passing motor vehicle and then had fallen asleep outside the Sydney Cricket Ground precinct.
[20] He was tasered and pepper-sprayed while still on the ground and then taken to the Sydney Police Centre in Surry Hills, where he was charged with six offences including two counts of assaulting an officer in the execution of duty, behaving in an offensive or indecent manner and remaining on trust lands after a request to leave.
The NRL released a statement saying "Scott's charges carry a maximum five years imprisonment and do not qualify for an automatic no-fault stand down.
[24] On 9 September 2020, five allegations made against Scott were dropped by police after bodycam footage showed him asleep and not resisting arrest.
Sutherland Shire Police began investigating Scott in November 2020 following reports of domestic-related assaults alleged to have occurred in 2018.