MINNEAPOLIS — The Minnesota Twins signed right-hander Rich Harden to a minor-league contract Friday with an invitation to compete for a spot on the staff in spring training.

The 31-year-old Harden sat out the 2012 season after surgery on Jan. 31 to repair the rotator cuff in his throwing shoulder, his latest setback in a long line of arm problems. Harden has the third-best strikeouts-per-nine-innings ratio in the majors since his debut with Oakland in 2003, behind only Tim Lincecum and Clayton Kershaw.

But Harden, after going 11-7 with a 3.99 ERA in 31 starts over 189 2-3 innings in his first full year in the majors in 2004, hasn’t surpassed the 150-inning mark since. Between the A’s and the Chicago Cubs in 2008, Harden finished 10-2 with a 2.07 ERA in 25 combined starts, posting 181 strikeouts in 148 innings. But he had a 5.58 ERA in 2010 with the Texas Rangers, accumulating only 92 innings and had a 5.12 ERA in 15 starts in his return to the A’s in 2011. Harden has been hit by a number of injuries, but the shoulder has given him the most trouble.

The 6-foot-1, 195-pound Harden was a 17th-round draft pick in 2000 out of Central Arizona College. The native of Victoria, British Columbia, spent seven years with the A’s. His career record is 59-38, with a 3.76 ERA and 949 strikeouts over 928 1-3 innings.

The Twins have acquired Vance Worley, Kevin Correia and Mike Pelfrey to join Scott Diamond in their rotation, which ranked last in the American League in ERA last season, but there’s one open spot. If Harden can prove he’s healthy and still effective, he’ll have a chance to be the fifth starter. Returners Nick Blackburn, Samuel Deduno, Cole De Vries, Liam Hendriks and Esmerling Vasquez will also be in the mix this spring. The Twins will have 34 pitchers in camp.

The Twins also announced that Diamond had arthroscopic surgery Tuesday to remove a bone chip from his elbow. The team said he’ll be ready for spring training.