The 29-year-old, who was called up to the Scotland squad for the 2008 Six Nations Championship, has moved to Sixways Stadium until at least the end of the 2009/10 season.
MacRae, who can play across the back line, has impressed on trial and featured in pre-season games with Doncaster Knights and Newport Gwent Dragons.
Director of Rugby Mike Ruddock said: "We are delighted that Calum has agreed to join us. He has been on trial for the past three weeks and has acquitted himself very well.
"He is an experienced and talented player who will add value to our squad, particularly as he has Heineken Cup experience, Magners League experience and has been captain of the Borders region in Scotland.
"Our experience last year, in terms of injuries to our three quarter line, has shown us that having a player like Calum around will be most useful.
"He can play at inside and outside centre and full back and has age group representative honours with Scotland at fly half.
"Calum joins us on a one-year contract and I'm sure that he will prove a very valued member of the squad."