Graham, from Australia, became Arizona's punter in December 2008 but was released just before the start of this season. Dave Zastudil has been the team's punter through the first four games of the season.
Coach Ken Whisenhunt said after Wednesday's practice that Zastudil has a sore knee and it's uncertain whether he will be able to play Sunday at Minnesota. Whisenhunt called Graham "an insurance policy."
In addition, safety Mark LeGree was released from the practice squad.