The Browns will receive a 2020 sixth-round pick in return, a source told ESPN’s Adam Schefter.
Taylor, 27, started 15 games for the 0-16 Browns in 2017. He had one forced fumble and a half-sack while appearing in all 16 games.
NFL Network first reported the trade.
Taylor could fill a need for the Cardinals, who have sought a cornerback to play opposite Patrick Peterson.
A 2013 second-round pick by the Miami Dolphins, Taylor has three career interceptions (all in 2016) over five NFL seasons. He joined the Browns in a draft-day trade in 2016.
Taylor would be the sixth player traded by new general manager John Dorsey since taking over the team in December.
The Associated Press contributed to this report.