Carson made his Leeds debut when coming on as a substitute in a 3-0 defeat against Middlesbrough on 31 January 2004. Paul Robinson was sent off in the eighty-eighth minute and Carson's first task was to try to save a penalty, but he didn't succeed. He was kept out of Leeds' starting line-up in the 2004/05 season by Neil Sullivan and wanted a new challenge. Liverpool won the race with Chelsea to sign the England u-21 keeper in January 2005. He was Dudek's understudy, but his quest to become Liverpool's number one keeper became considerably more complicated with the arrival of Jose Reina in July 2005. After only nine games in two years, including a great performance in the quarter-finals of the Champions League against Juventus at Anfield, he went on loan to Premiership side Charlton who got relegated. Benítez wanted to keep Carson at Anfield but he was still in England's plans and could not afford to be an unused understudy: "I am happy with the situation and for Scott to play regularly somewhere else. We do not want to lose him, certainly not sell him." said Rafa in August 2007.

Carson was on loan at Aston Villa throughout the 2007/08 season but Martin O'Neill's side didn't take up the option to sign him and brought in Brad Friedel instead. When Carson left Liverpool for good he preferred Premiership newcomers West Bromwich Albion to Stoke in the summer of 2008 which didn't seem such a wise choice when Stoke finished twelfth in the Premier League and WBA were relegated. Baggies manager Roberto di Matteo made Carson club captain at the start of the 2009/10 season. "Scott has the respect of all the other players. He gives his best in every training session and every game," said the Italian. Carson featured in 40 of 46 matches in the Championship as the West Midlands club made an immediate return to the Premier League. Carson's form dipped halfway through the 2010/11 season and he was replaced for a few matches for Boaz Myhill, but Carson was back in favour with the arrival of Roy Hodgson in February 2011. Early July 2011 Carson completed a surprising transfer to Turkish club Bursaspor.

Carson played in twenty-nine of the thirty-four Süper Lig matches in the 2012/13 season. Bursaspor finished in fourth position, which meant that they qualified for the Third Qualifying Round of the Europa League. After two years in Turkey, the 27-year-old Carson returned to the English game by signing a three-year contract with Wigan Athletic. He made 26 appearances in Wigan's goal during the 2013/14 season and remained there for 2014/15 but after their relegation from the Championship, he signed for Derby County, appearing 36 times as they reached the playoffs. In both 2016/17 and 2017/18, he was an ever-present on goal for Derby in the Championship. In the second half of 2018/19 Carson was dropped by Frank Lampard and did not look likely to regain his place under new manager Philip Cocu after Lampard's departure for Chelsea. His next destination was a shock to all, however, when he joined Manchester City on a one-year loan deal on 7 August. Despite not making a first team appearance for City in 2019/20, Carson agreed another season long loan at the Etihad Stadium for 2020/21 and made one league appearance. When his Derby contract expired he joined City on a free transfer for 2021/22 and came off the bench for the last seventeen minutes of a Champions League round of sixteen game at home to Sporting Lisbon, when City were 5-0 up on aggregate. This was sixteen years and 338 days after he had last appeared in the competition for Liverpool, the longest gap between appearances in its history. During the next two seasons Carson remained at City as third choice, without making an appearance. He signed a one year contract to keep him there for 2024/25, telling the club website "Every day I work hard and learn something new from Pep [Guardiola], [goalkeeping coach] Xabi Mancisidor and the world class group of players. Hopefully I can continue to help our goalkeepers perform at their best as we challenge for even more trophies". He left City at the end of that season, having been part of squads that lifted twelve major honours.