The 26-year-old Peterson played in 14 games last season and started three after being pushed into a bigger role because of Patrick Peterson's six-game suspension and Robert Alford's season-ending injury.
He had 16 tackles, two passes defended and six special teams tackles after joining the team off waivers from the Rams in September.
The 5-foot-11, 185-pound Peterson came into the league as an undrafted rookie free agent in 2016.
The Cardinals also announced that they released cornerback Andre Chachere. He spent two different stints with Arizona on the practice squad last season.