Vielma, 23, can play second base, third base and shortstop, which is his primary position. He's a .256 hitter in six Minor League seasons.
This year, Vielma hit a combined .229/.273/.280 in 121 games between Double-A Chattanooga and Triple-A Rochester. He was designated for assignment by Minnesota on Tuesday.
Chris Haft has covered the Giants since 2005, and for MLB.com since 2007. Follow him on Twitter at @sfgiantsbeat and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.