The 30-year-old has not played for the Pilgrims since the final game of last season and will stay with the Lambs until January 1.
"I've been honest with Chaddy all along," manager John Sheridan told the club's official website.
"He's an experienced player and it's only right that he should be playing.
"Even though Tamowrth are in the Conference, it's a very tough league now so he'll go there and get a few games under his belt."
- Sports & Recreation