Chicago optioned reliever Brooks Raley to Triple-A Iowa to make room for Rodriguez on the roster.
Rodriguez pitched in 17 games with the Nationals and went 0-1 with a 4.00 ERA. He gave up 14 hits in 18 innings pitched and had 11 strikeouts and 16 walks.
Cubs manager Dale Sveum said Rodriguez will be a middle-inning reliever for now, but the Cubs eventually want to build him up so he can pitch two innings if Chicago needs him to.
"To start out with, he'll be a middle guy," Sveum said. "Winning or losing, we'll see what we got. We'll try to get him built up, we need him to be able to go two innings. But that's what we're looking for -- a power arm to be able to do both and eventually fall into even a bigger role."
Chris Iseman is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.