Cropper joined Southampton in August 2012. Cropper served as a backup keeper for the Saints; making the first team bench, but playing for the U-21 and U-23 teams and never making a first team appearance. His time with Southampton included multiple injuries. After 3 years at the south coast club, Cropper was released.
On June 30, 2015, Cropper joined newly promoted Championship side Milton Keynes Dons. He made his debut for MK Dons on August 11, 2015 in an EFL Cup first round win against Leyton Orient. In September Cropper underwent knee surgery that kept him sidelined for over a month. On April 16, 2016, Cropper was sent off for a foul on Preston North End's striker Eoin Doyle. He returned from the suspension on April 23 and suffered a season ending shoulder injury in a 4–1 loss to Brentford. Cropper was released after the 2015-16 season when the club decided not to take up the one-year option in Cropper's contract after being relegated to League One.
On August 18, 2016, Cropper signed with Major League Soccer club New England Revolution. He made his Revolution debut on October 23, getting a clean sheet in a 3–0 win over the Montreal Impact in the final game of the season. The Revolution's first choice goalkeeper, Bobby Shuttleworth, was traded to Minnesota United ahead of the 2017 season, giving Cropper a shot at the starting job. Cropper impressed head coach Jay Heaps and won the starting job coming out of preseason. He started 28 of the 34 league games during the year, keeping 8 clean sheets. However the Revolution finished in 7th place in the Eastern Conference, missing out on the playoffs by 5 points. Cropper did not play during the 2018 season. He missed the start of the season due to a concussion. When he had returned to action, head coach Brad Friedel kept Matt Turner as the starter with Brad Knighton as the second choice keeper. Cropper made his first appearance of 2019 on March 30, a 2–1 win over Minnesota United in the 5th game of the season. He would start the next 7 games for the Revs before Friedel decided to bench him. Bruce Arena came in as the new head coach, but Cropper failed to return to the lineup.
On August 17, 2019, Cropper was loaned to USL Championship side Hartford Athletic for the remainder of the season. He made his debut for Hartford on August 24, a 3–2 win over Atlanta United 2. Cropper started the final nine games of the season for Hartford, keeping one clean sheet. On November 21, 2019, New England declined their contract option on Cropper.
Houston Dynamo
On January 24, 2020, Cropper signed with MLS club Houston Dynamo.