Rodriguez, who turns 36 Sunday, will attend big league spring training and compete for the fifth spot in the rotation. If he is added to the 40-man roster, he would get a one-year contract for $2 million.
Rodriguez was 0-2 with a 6.75 ERA last year in six starts with Pittsburgh, which released him on May 30. Rodriquez appeared in only 12 games in 2013 due to a left forearm injury.
Beginning in 2008, Rodriguez posted six straight seasons with an ERA under 4.00 with Houston and Pittsburgh. His has a 91-94 record with a 4.06 ERA in 248 starts and 10 relief appearances.