The Saving Private Ryan writer is reworking the first draft by Don Payne, who worked on the first Thor screenplay, according to Deadline.
Game of Thrones writer Alan Taylor was recently announced to helm the movie after previously attached director Patty Jenkins was dropped from the project.
The film will see Thor stars Chris Hemsworth, Natalie Portman and Tom Hiddleston reprise their roles. Hiddleston and Hemsworth will also feature in Joss Whedon's upcoming Avengers movie.
Rodat has most recently been working on the television sci-fi drama Falling Skies, and also wrote the Oscar-nominated historical war movie The Patriot, starring Mel Gibson and Heath Ledger.
Thor 2 is expected to begin shooting in the summer, with a release date scheduled for November 15, 2013. It is currently unclear whether the rewrite will affect this schedule.
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