The Cardinals signed Jones to a reserve/future contract Monday, Darren Urban of the team's official site reports.
Davis is a four-year NFL veteran who has seen action with three different teams, including two stints with New Orleans, over the past two campaigns. He played a prominent role in Weeks 2 and 3 with the Saints this season, tallying 65 yards and two touchdowns on 20 rushes along with 21 yards on four receptions, but he was released two weeks later. Jones subsequently signed with Arizona and spent much of the remainder of the campaign on the practice squad but did see action in three games, carrying five times for 25 yards and adding three catches for 16 yards. He'll have a chance to complete for a spot on the team's roster during training camp this summer.