Last season, Rodriguez pitched for the Nationals and Cubs, and in 22 innings, he walked 20 while striking out 12.
A Venezuelan native, Rodriguez broke in with the A's in 2009. In parts of five big league seasons, he is 5-7 with a 4.24 ERA in 148 appearances. Rodriguez has 150 strikeouts and 102 walks over 148 2/3 innings.
Miami also announced that second baseman Avery Romero, the team's third-round pick in the 2012 First-Year Player Draft, has been extended an invitation to Major League camp.
The Marlins now have 64 players set to participate in Spring Training, which gets underway with pitchers and catchers workouts on Feb. 16 in Jupiter, Fla.
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter @JoeFrisaro. This story was not subject to the approval of Major League Baseball or its clubs.