Bradley has struggled since returning from a sinus fracture caused by a line drive that hit him in the face on April 28.
The 22-year-old failed to pitch past the fifth inning in four starts since coming back, going 0-3 with a 7.42 ERA. He allowed five runs on eight hits in five innings in a loss to Atlanta on Monday.
Ray made one appearance with the Diamondbacks earlier this season, allowing a run in five innings before being sent down to Reno. He is expected to start Thursday night against the New York Mets.