Having joined Manchester United's academy at the age of six, Rothwell signed professional terms with the club in the summer of 2013.[3] On 26 July 2011, he scored twice in a 7–0 win over County Tyrone in the Milk Cup.[4] He was named as a substitute for a first-team game against Watford in March 2016.[5]
On 27 January 2015, Rothwell joined Blackpool, then in last place in the Championship, on loan for the remainder of the season.[6] Four days later he was included in a professional matchday squad for the first time, remaining an unused substitute for Blackpool's 1–0 win over Brighton & Hove Albion at Bloomfield Road.[7] A week later he made his debut as Blackpool lost 4–0 away to Norwich City, replacing Mark Waddington at half time.[8] His first career start came on 24 February, playing the entirety of a defeat by the same score at Brentford, his last of three appearances for the club.[9]
On 18 July 2015, Rothwell joined League One side Barnsley on a six-month loan.[10] He played four League games (two as a substitute) and made one appearance in the opening round of the Football League Trophy,[11] a competition Barnsley ultimately won, beating Oxford United.[12]
Oxford United
On 12 July 2016, Rothwell joined Oxford on a two-year deal after turning down the offer of a new contract at Manchester United.[5] He scored the first senior goal of his career in an FA Cup second-round replay against Macclesfield Town on 13 December 2016, a game which Oxford won 3–0.[13] His first league goal came in a 5–1 win over Bury on 28 March 2017.[14]
Blackburn Rovers
On 22 June 2018, Rothwell joined Blackburn Rovers for an undisclosed fee. He signed a three-year deal.[15][16]
At the end of the 2021–22 season it was announced that Rothwell would be leaving the club upon the expiration of his contract.[17]
On 15 January 2024, Rothwell joined Southampton on loan for the remainder of the 2023–24 season.[19] Five days later, he made his first appearance for the club in a 1–3 victory against Swansea City, replacing Stuart Armstrong in the 76th minute.[20] He scored his first two goals on 10 February 2024 for the club in a 5–3 victory against Huddersfield Town.[21] Rothwell later received the Sky Bet Championship Goal of the Month for February for his first goal in that game.[22][23]