I live in Texas. Can a credit card creditor place a writ of garnishment on my bank account for an unpaid debt?

First of all a credit card company can not put a garnishment on your account ONLY a court judgement can. I am not sure what the laws are in Texas but in some states once a judgement is entered attachments and garnishmnent are sure to follow. Check the laws in your state Some will not allow wage garishmnent but will allow bank accounts to be attached once a judgement is entered