Fogbugz/Kiln had a variation of this. You could easily see which branches a particular commit was in and it was tied back to the ticket as well. It didn't influence ticket state, but it was easily cross-referenceable.
I loved it! Unfortunately, I was overruled about three years ago and against (quite strong) protesting on my part, we left it for Easy Redmine (strong dislike).
I have no idea what it is like anymore since it is no longer under to stewardship of Joel, and it's been quite a while since I used it.
Fogbugz, now known as Manuscript, is pretty good. It is somewhere between overly simple (Github Issues) and overly complicated (JIRA).
I like it way better than JIRA (having said that, I haven't used JIRA in years).
If you're a startup, you used to be able to get a two-user account for free -- not sure if they still do it, as Manuscript/Fogbugz got acquired by another company recently.
