The Browns had waived Harrison on Wednesday. He was not at the team's mandatory minicamp on Tuesday, and coach Freddie Kitchens said when asked about Harrison's absence that the player had missed his flight and gotten to camp late.
Harrison, who joined the Browns as an undrafted free agent last season, started eight games at left tackle in 2018.
The Cardinals released offensive lineman Andrew Lauderdale on Thursday to create a roster spot for Harrison.
Lauderdale signed with the Cardinals in April after spending time with New Orleans, San Francisco, Buffalo and the Arizona Hotshots of the Alliance of American Football. He went undrafted out of New Hampshire in 2017.
The Associated Press contributed to this report.