Where do you think rights come from, if not God?
We get rights from ourselves. Society generates them.
First, one must understand what a "right' is. It's an allowance from the society one is within, as to what one can do, or what entitlements a person has. A right isn't something you should be able to do, but something you are able to do.
For instance, the U.S. government grants its citizens the right to free speech. It's entirely dependent on where one is located. This right to free speech ceases for a person once he or she enters a country that doesn't guarantee it.
To say that they're God-given rights isn't accurate - because, one would think these God-given rights would be ubiquitous... but they aren't.
Additionally, where in the Bible does it say one has a right to free speech, or the right to due process, or the right to remain silent? Those came from the people in the countries who produced them, not the Bible. If we're capable of creating rights, why does a supernatural entity need be involved at all?
We, as a species, are capable of establishing rights ourselves. Many people seem to get hung up on the idea that "rights" either aren't valid, or don't exist, unless they come from some supreme authority or "ultimate" source.
They're partially correct - rights aren't worth the paper they're written on, if they aren't enforced. Humans do the enforcing (most of the time).