In exchange for Rodriguez, the Braves received minor league first baseman Connor Joe.
Rodriguez played for the Pirates during the 2015 and 2016 seasons, setting career highs last season with a .270 batting average, 18 home runs and 56 RBIs.
He only played 15 games this season with the Braves after starting on the disabled list while recovering from left shoulder surgery to repair injuries sustained in an offseason automobile accident.
Joe was selected with the 34th overall pick in the 2014 MLB draft. He was hitting .240 with five home runs this season for Double-A Altoona.
In other moves, the Braves recalled left-handed pitcher Max Fried from Double-A Mississippi, recalled infielder/outfielder Jace Peterson from Triple-A Gwinnett and optioned RHP Jason Hursh to Gwinnett.
The Pirates also claimed right-handed pitcher George Kontos off waivers from the Giants.