The Arizona Cardinals are not going to be receiving any compensatory draft picks. Compensatory draft picks are handed out to teams that lose more free agents then they bring in, but that didn't happen for Arizona, who brought in more free agents then they brought in.
Arizona, Seattle and San Francisco didn't receive any compensatory picks; only the St. Louis Rams got any picks out of the NFC West team, and it was a low rounder in the 7th round. Not too significant in the big picture.
The Cardinals get the 13th pick overall in the first round in the 2012 NFL Draft and have a full slate of picks though, so there's no real reason to grab picks. The Cardinals don't really need to replenish the coffers either with multiple picks as they have plenty of solid talent, just land some top-line talent early on.
To discuss the draft picks for the Cardinals, head on over to Revenge of the Birds.