Stanzi has previous stints with the Houston Texans, Jacksonville Jaguars and Kansas City Chiefs.
Stanzi spent two seasons on the Chiefs' active roster but did not play in a regular season game.
Stanzi started 35 games at Iowa and posted a 26-9 record as a starter, completing 542 of 907 passes for 7,377 yards.
Follow me on Twitter: @AaronWilson_NFL Aaron Wilson covers the Texans for The Houston Chronicle.