Calder joins Rovers on loan
Calder also had a spell earlier this term on loan at Scottish Premier League club Dundee.
Calder, who joined Villa at the age of nine in 2005, was part of the Villa's U19 side that won the 2012/13 NextGen Series, beating Chelsea in the final of the competition.
Competent in defence or midfield, Calder has represented England at U17 level, playing at the 2012 Nordic U17 Football Championship in the Faroe Islands.
He made four appearances including the final as England came runners-up to Sweden.
Calder will now link up with Darren Ferguson's side at the Keepmoat Stadium for the rest of their League One campaign.
They lie 18th in the table as they look for progress up the 24-team league.