This is actually a complex one, because the word "marries" isn't necessarily correct in Lev 20:21. The translations I would generally consider more reliable (KJV, ESV, YLT etc) translate it "takes", not "marries". The Hebrew word can mean "to take, get, fetch, lay hold of, seize, receive, acquire, buy, bring, marry, take a wife, snatch, take away" - so it could be talking about marriage, but not necessarily.
Read it in context. This and the preceding verses are all about the crime of "uncovering nakedness". The context is described as if a man should "take" (v17, v21), "lie with" (v18, v20), or just uncover nakedness with no further description of context (v19). These verses are not discussing marriage, but uncovering the nakedness of women who are close relatives. Leviticus 18:16 is also "Thou shalt not uncover the nakedness of thy brother's wife" - it's discussing exactly the same thing.
Both passages are essentially saying either "don't see your brother's wife naked" (if we go by the KJV), or "don't have sex with your brother's wife" (if we go by the NIV). It's not about marriage, but adultery, quite a different situation.
Why would this be forbidding marrying your brother's wife? Can you even do that? Isn't that impossible unless she is polyandrous? Because you can't marry her while she's married to him, and if she ceases to be married to him she isn't his wife any longer so you're not marrying his wife.
These verses are very clear that you can't see her naked when she's married to your brother - that would be adulterous. So when does she cease to be your brother's wife? Clearly on his death she ceases to be his wife, or else the Levirate law would contradict this. So even a brother's wife is freed by his death and is available for you to marry (with that even being required in some circumstances). So the question posed by Cecil is simply "Does divorce also cause her to cease to be your brother's wife, or not?"
Deuteronomy 24:1-2 are clear that a legitimately divorced woman may go and be another man's wife, she is no longer the wife of the first man. Is there any scriptural reason to think that there is still some tentative tie held to her after a man divorces her, which makes her still counted as his wife from his brother's perspective, but not his wife from the perspective of any other man?
So to answer Cecil's original question - I can't see any reason why if she's TRULY divorced she isn't available to you.
BUT that doesn't mean it's necessarily a good idea! Why did your brother divorce her? If she committed adultery for instance, you've got to wonder whether she'd be a suitable wife. Furthermore, you're probably somewhat similar to your brother, if he couldn't get on with her that's a good reason to think you might hit the same issues also. And the family relationships would get terribly complicated. Just because something may be permissible doesn't mean it's a good idea.
Why do you ask? :?
