Turner was given the right-of-first-refusal tender of $2.1 million, giving the Cardinals the right to match any offer. Gardeck received a second-round tender that is worth $3.38 million this season.
Turner, 24, has played all 16 games two of the past three seasons in becoming a core special teams player. He appeared in 12 games in 2019.
Last season, he saw action on only six defensive snaps but 348 on special teams. In his three seasons, Turner has played 29 defensive snaps and 988 on special teams.
He has 37 career tackles, including 14 in 2020.
The Cardinals also tendered exclusive rights free agent linebacker Kylie Fitts.