Alcock made his temporary switch to the Keepmoat last month in a bid to regain his fitness after suffering an injury in the September clash between the Blades and Rovers.
The 27-year-old has started the last four games for Rovers, operating at both right sided centre half and wing back.
It was expected that his deal would be extended given a lack of first team opportunities with the Blades and Rovers' lack of defensive cover.