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.
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 is the sixth player traded by new general manager John Dorsey since taking over the team in December.
The Associated Press contributed to this report.