The Cardinals gave up a conditional 2014 draft pick and swapped one of their sixth-round picks this year for Oakland's seventh-round selection.
Palmer, who agreed to rework his contract with the Cardinals, is expected to move into the starting quarterback role for new Arizona coach Bruce Arians.
The Raiders were at least able to get something for the quarterback rather than just release him. Oakland acquired quarterback Matt Flynn on Monday in a deal that sent two draft picks to the Seahawks.
Earlier, the Cardinals signed free agent quarterback Drew Stanton, the backup to Andrew Luck last season at Indianapolis, where Arians was interim head coach.