The deal is subject to a 24-hour recall clause, should they need his services back at The Riverside.
Stockdale has fitted in well with the Millmoor club, having played in six matches for Ronnie Moore's side in his first four weeks with the club.
Meanwhile, The Millers have confirmed they are not in the market to sign Newcastle United midfielder Bradley Orr, despite Rotherham being strongly linked with trying to land his services.
