Butler punted in all 16 games for the Pittsburgh Steelers as a rookie in 2012, averaging 43.8 yards per kick with 26 inside the 20-yard line. He was out of football in 2013 after being cut by the Steelers at the end of preseason.
Butler was with the Detroit Lions this preseason but was released on Aug. 25.
Butler is the son of former Cardinals and Chicago Bears kicker Kevin Butler.
The Cardinals had listed Zastudil as questionable for Monday night's season opener against San Diego.