I've used git-blame to find a particular commit. Now I want to find the branch that it originally came from. (From there, I'll use the branch name to find the particular ticket)
Let's define "original branch" as "the branch to which the commit was made before the branch was merged into any other branch".
Like the others said, if the branch you are looking for isn't local to the repository on which you are blaming this commit (e.g. a branch only in the personal repo of a distant developer), you are screwed.
But assuming that sought-after branch is something you can see, and that of course you have the commit's hash, say
d590f2..., a partial answer is that you can do :
$ git branch --contains d590f2 tests * master
Then, just to confirm you have the culprit:
$ git rev-list tests | grep d590f2
Of course, if
d590f2 has been merged in more than one branch, you will have to be more subtle than this.