Sigsworth, aged seven, started her youth career playing for Branton Boys, before moving to Doncaster Rovers Belles Juniors. She then moved to Sheffield United Girls’ Centre of Excellence, where she broke into the England under-17 squad. After three seasons, she returned to Doncaster Belles.
Doncaster Rovers Belles
Sigsworth began her senior career by signing with Doncaster Rovers Belles in 2011. She made her senior debut on 23 July 2011 in a 3–0 defeat against Birmingham City. In four years, she scored seven goals in 41 appearances.
Notts County
In January 2015, Sigsworth moved to FA WSL outfit Notts County. However, she struggled to make the bench and never made an appearance.
Return to Doncaster Rovers Belles
In November 2015, Sigsworth re-signed with hometown team Doncaster Rovers Belles ahead of the 2016 season. On 20 March 2016, she scored her first goal, in her first appearance since returning to the club in a 4–1 defeat against Chelsea in the FA Women's Cup. In May 2016, she signed a full-time contract. In August, she suffered a cruciate knee ligament injury, missing the rest of the season, as the team were relegated to FA WSL 2, as well as the subsequent Spring Series. In the 2017–18 season, Sigsworth won the FA WSL 2 Player of the Month award for March. By the end of the season, Sigsworth had guided Doncaster to the FA WSL 2 title and won the golden boot with 15 goals.
Manchester United
In July 2018, Sigsworth was announced as part of the inaugural Manchester United squad that was set to compete in the newly restructured FA Women's Championship. She made her competitive debut for Manchester United in a 1–0 League Cup victory against Liverpool on 19 August. On the opening day of the 2018–19 Championship season, Sigsworth scored five goals in a 12–0 win away to Aston Villa. On 9 March 2019, during a 2–0 FA WSL Cup win against West Ham, Sigsworth was involved in an incident with Brooke Hendrix; three days later, Hendrix was charged with violent conduct by the FA and banned for three games. Sigsworth finished the season with consecutive Championship titles and golden boot awards, having scored 17 league goals. Sigsworth scored her first goal of the 2019–20 season in United's 2–0 League Cup win against Manchester City on 20 October 2019. Ahead of the 2020–21 season, Sigsworth signed a new one-year contract with an option for a further year.