The A's announced the deal, which includes $425,000 guaranteed, on Saturday.
Parker has had lousy luck the past two seasons, not pitching in the majors since 2013. He missed the 2014 season following his second Tommy John surgery, fractured the elbow during a May rehab start to end his comeback bid and had another procedure from Dr. James Andrews. Oakland's brass has been encouraged by his progress this offseason.
Parker, 27, is 25-16 with a 3.68 ERA in two-plus major league seasons: 2012 and 2013 with the A's after one outing for Arizona in 2011.