Baker, 31, signed a one-year deal for $5.5 million with another $1.5 million possible in performance bonuses this past winter.
This season Baker posted a 1-2 record, 6.17 ERA, and 14 strikeouts in 23 1/3 innings with Class A Kane County.
Baker has pitched all or part of the last seven season with the Minnesota Twins, from 2005-11. He was the Twins’ Opening Day starter in 2010 and made 23 appearances in 2011, limited by a right elbow injury that required Tommy John surgery.
He did not pitch during the 2012 season.
The Twins all-time pitching record books feature Baker in multiple categories, including winning percentage (fourth with .568), starts (11th with 159), wins (11th with 63), and strikeouts (11th with 770).
Baker was drafted by the Twins in the 2003 MLB amateur entry draft in the second round (58th overall).