Congratulations. I don't see why you couldn't. Prisoners under a death sentence in California can get married, so your warrant would stop the process.
Do you think you might get arrested at the clerk's office? I think it is highly unlikely. I'd stay away from the DMV, though. You will also not be able to get a passport or leave the country, so if you're planning to honeymoon in Cabo San Lucas, cancel those reservations.