The Canadian club, managed by former Rovers captain Ryan Nelsen, have taken the defender on loan until December, with an agreement in place to make it a permanent move.
Signed from Queens Park Rangers in January 2012, Orr has made 34 appearances for Rovers. Last season saw the full-back spend three months on loan with Ipswich Town.
This term, he spent a short spell on loan with Blackpool, but injury forced an early return to Rovers.
Toronto get their MLS campaign underway on March 15th against Seattle Sounders.