Parker was given an $850,000 salary on Saturday by Elizabeth Neumeier, Robert Herzog and Mark Irvings instead of his request for $1.7 million. The sides argued their positions a day earlier.
A 26-year-old right-hander, Parker was sidelined after getting hurt during spring training and having elbow ligament-replacement surgery for the second time.
Parker made his big league debut with one appearance in 2011 and is 25-16 with a 3.68 ERA in 62 starts. A first-round pick selected ninth by Arizona in 2007, Parker was obtained from the Diamondbacks in a December 2011 trade that sent All-Star Trevor Cahill and reliever Craig Breslow to Arizona.