Boston acquired Robertson and Justin Hagenman from the Dodgers in exchange for Enrique Hernandez on Tuesday, Jeff Passan of ESPN.com reports.
Robertson has struggled to a 6.10 ERA in nine relief appearances this season at the MLB level, but he boasts a 2.54 ERA and 42:9 K:BB in 28.1 innings of work at Triple-A. The 25-year-old right-hander could maybe get some high-leverage looks with the Red Sox down the stretch, though it's unclear yet whether he'll report directly to Boston or head to its Triple-A affiliate in Worcester.