Parker, 27, has made 29 appearances for the Latics this season, scoring two goals, and will stay at Gigg Lane until April 17.
The Shakers hope his arrival will give their play-off push a significant boost after a paltry return of just one goal in their last five matches.
Parker could earn a starting role against the Millers as Ryan Lowe begins a three-match ban for being sent off in last weekend’s 2-0 defeat at Macclesfield.
Skipper Stephen Dawson missed that game because of a family bereavement but is back for the clash with Ronnie Moore’s men.
Striker Danny Carlton is still recovering from a long-term Achilles injury and remains sidelined, along with Paul Scott (knee) and Damien Allen (groin).