Is there a word that means "the wife of one's brother"?
That would be sister-in-law:
sister of one's spouse, the wife of one's brother, or sometimes the wife of one's spouse's brother.
Edit: as ShreevatsaR points out in the comments, if you're looking for a single word that means only "wife of one's brother" and nothing else, then you're out of luck.
Sister-in-law: it can be the sister of your spouse, or the wife of your brother or brother-in-law.