The Cardinals claimed offensive lineman Blaine Clausell, defensive tackle Garrison Smith and offensive lineman Jeremy Vujnovich.
Vujnovich started all 16 games at left guard for Indianapolis last season after appearing in two games for the Colts in 2016.
Arizona also signed free agent defensive end Zach Moore.
The Cardinals waived injured defensive end Vontarrius Dora and safety A.J. Howard and released offensive linemen Evan Boehm and Will Holden.
In addition, the team has re-signed offensive lineman Will House, defensive end Alec James, quarterback Charles Kanoff, running back Elijhaa Penny, defensive tackle Pasoni Tasini, wide receiver Jalen Tolliver and tight end Andrew Vollert to the practice squad.