People do that. I have an inalienable right to breast feed a baby in public, many women say. I have a right to be a homosexual. Animals have rights to live. You'll usually get a silence when you ask such a question.
Rights are just claims to things.
They're a claim to something that justice gives you. Now, you can't have justice without a law. And so you can't have rights without higher laws that establish this entitlement. But if there is no God, it's hard to imagine how one might have a higher law. I have a right to receive half of your income for Stand To Reason.