The 24-year-old has an option remaining on his contract and is a candidate to start the season at Triple-A Buffalo. Another scenario could see Oramas competing for a spot in Toronto's bullpen, but with a couple of late-inning relievers still needed, that seems unlikely.
Albers received an invitation to Spring Training after spending the 2014 season with the Hanwha Eagles of the Korean Baseball Organization.
The native of Saskatchewan made his Major League debut with the Twins in 2013 and went 2-5 with a 4.05 ERA in 10 starts. Albers previously represented Canada in the 2011 Baseball World Cup and won a gold medal at the Pan American Games in 2010.
Gregor Chisholm is a reporter for MLB.com. Read his blog, North of the Border, and follow him on Twitter @gregorMLB. This story was not subject to the approval of Major League Baseball or its clubs.