In the state of Texas if your car is voluntarily repossessed can they sue you for a deficiency judgment and charge it to your credit card without your permission?

Yes, they can sure you for any monies still owed on the vehicle. No, nobody can charge anything to your credit card without your permission. But beware, there may well be some clause worked into the mice-type on the agreement that you never even noticed was there. Go over any paperwork you have; if you don't see anything about implied permission given for them to charge your account, dispute the charge with your credit company and file a formal complaint.