Rossington scored his maiden first-class century when he made 103 not out off 57 balls against Cambridge University on 24 April 2013. This innings included 7 sixes and one passage of 10 balls yielded 48 runs.
In 2014 Rossington played for Northamptonshire while on loan from Middlesex. At the end of that season he signed a contract with Northamptonshire.[6] In August 2016 he was part of the Northants team that beat Durham to win the Twenty20 title.[7]
In 2022 Rossington joined Essex on a season long loan.[8] In April 2022, he was bought by the London Spirit for the 2022 season of The Hundred.[9] In June 2022, Rossington signed a three-year contract with Essex.[10]
Rossington made his debut for England Under-19s against Sri Lanka Under-19s during their tour to England in 2010, playing in two Youth Twenty20 Internationals.[11] England Under-19s toured Sri Lanka in the early part of 2011, with Rossington playing a single Youth Test match on the tour,[12] He scored 113, his hundred coming off 165 balls, with 12 fours and 2 sixes; he also made a stumping in the match.[13]