Allen (0-1) was tagged with Thursday's loss, allowing one run on three hits and one walk while striking out three over 4.2 relief innings against the Giants.
The Diamondbacks selected Allen's contract from Triple-A Reno on Wednesday.
Allen was released by the Rockies on Sunday, Mark Feinsand of MLB.com reports.
Allen has submitted a 6.87 ERA, 1.60 WHIP and 21:6 K:BB across 18.1 innings through nine appearances with Triple-A Albuquerque this season.
Allen signed a minor-league contract with the Rockies on Friday.
The Orioles released Allen on Monday.
Allen cleared waivers Friday and was assigned to Triple-A Norfolk, Roch Kubatko of MASNSports.com reports.
The Orioles designated Allen for assignment Tuesday.
Manager Brandon Hyde said Sunday that Allen will work out of the bullpen to begin his time with the Orioles, Roch Kubatko of MASNSports.com reports. "I think we're always open for options, but he'll start out in the bullpen, and I'll try to get him a lower-leverage situation early just because he hasn't pitched in a while," Hyde said of Allen. "Looking forward to seeing what he can do. We really like his arm."
Allen was claimed off waivers by the Orioles on Thursday, Ryan Lewis of the Akron Beacon Journal reports.