Drake, 29, takes the roster spot of infielder Paul Janish, who was outrighted off the 40-man roster, Showalter said.
Drake was named the International League Pitcher of the Week last week, and has a 2.02 ERA with 42 strikeouts in 26 2/3 innings over 27 appearances. He hasn’t allowed an earned run over his past 14 outings.
"He’s been pitching really well for an extended period of time," Showalter said. "He’s very deserving. A lot of guys there have been."
Showalter said Duensing, who last pitched Sunday, had a scan on his elbow Monday in Texas during the game. He wasn’t available for that game, and Showalter said doctors in Baltimore were doing further evaluations Tuesday.
"Unless I get something completely different from what we’re thinking going in from the tests they’re doing tonight, he probably won’t be available tonight," Showalter said.
The bullpen has also been a man short since reliever Darren O'Day went on the disabled list on June 3 with a strained hamstring.
Janish, who hit .194 with a double and a .512 OPS in 14 games, has three days to decide whether to rejoin Triple-A Norfolk or elect free agency. He already cleared waivers, Showalter said.
"I’m fond of everybody who does what they do for us, and we’re very picky about who we let wear the black and orange," Showalter said. "Paul's a pro. Hopefully, he’s going to go home and take his options under consideration. … He’s still a part of the organization as we speak."
The move leaves Pedro Alvarez as the only infielder available in reserve until Manny Machado’s suspension ends after Wednesday's game. Janish was made surplus by the return of shortstop J.J. Hardy, who came back from a fractured foot Saturday.