Rodriguez has been on the disabled list since June 6 with stiffness in his left forearm, though he was also found to have arthritis in his elbow when examined by orthopedist James Andrews last month.
The Pirates made the move Saturday.
Rodriguez made 12 starts for the Pirates this season, going 6-4 with a 3.59 ERA.
The 34-year-old Rodriguez can become a free agent at the end of the season but also holds a $14 million player option in his contract to return in 2014.
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