I think the problem would be that there are already a lot of bugs reported on this forum. Therefore, migrating those bug reports to a bug tracking software/platform would mean a lot of work. Having both available for reporting, the forum and the tracker, and having to maintain both of them at the same time may be even more time consuming.
That said, I know from some experience in the company I work in that “Redmine” (http://www.redmine.org/) works relatively well, is open source and has Git integration (although it’s not that easy to set up correctly).