Rushworth started his career with Huddersfield Town before being released at 16; he subsequently joined the academy of FC Halifax Town, before being signed by Brighton & Hove Albion in 2019.[3] He signed for Worthing on a season-long loan in August 2019.[4] He made 30 appearances in all competitions for the seventh tier side.[5]
He signed a new three-year contract with Brighton in July 2020.[6]
Rushworth moved on a season-long loan to League Two side Walsall in July 2021.[7][8] He made his debut for the club on 7 August 2021 in the 1–0 away loss at Tranmere on the opening game of the 2021–22 season in what was also his Football League debut.[9] On 5 January 2022, whilst on loan at Walsall, Rushworth signed a new contract with Brighton, committing to the club until 2025.[10]
He signed on loan for Championship outfit Swansea City on 31 July 2023 for the 2023–24 season.[14][15] He made his debut five days later, denying a late Ivan Šunjić winner with a superb save in the 1–1 home draw against Birmingham City.[16] In Rushworth's second Championship game for the "Swans", he scored an own goal after the ball rebounded off the crossbar into him, putting West Bromwich Albion back ahead in the eventual 3–2 away loss.[17] At the end of the 2023–24 season, he was named both Supporters' Player of the Year and Players' Player of the Year.[18]
On 30 August 2024, Rushworth once again moved to the Championship, joining Hull City on a season-long loan.[19][20]