Texas Family Code section 2.202 allows the following people to perform the ceremony and sign the license:
(1) a licensed or ordained Christian minister or
priest;
(2) a Jewish rabbi;
(3) a person who is an officer of a religious
organization and who is authorized by the organization to conduct a
marriage ceremony; and
(4) a justice of the supreme court, judge of the court
of criminal appeals, justice of the courts of appeals, judge of the
district, county, and probate courts, judge of the county courts at
law, judge of the courts of domestic relations, judge of the
juvenile courts, retired justice or judge of those courts, justice
of the peace, retired justice of the peace, or judge or magistrate
of a federal court of this state.
Anyone who doesn't meet one of those requirements can't do it and make it legal. That being said, you can still have a common law marriage in Texas without a ceremony.
