It depends. Texas is one of a handful of states that still recognizes common law marriages. Therefore, if you meet the statute of a common law marriage, then, yes, you may file a return as Married Filing Joint.
Remember, though, that this does make you married in Texas, which also puts you under the Community Property Laws. The following website can help you to determine if your relationship qualifies as a common law marriage: http://guides.sll.texas.gov/common-law-marriage
Likewise, this website provides information on TX Community Property Law: https://www.prater-ridleylaw.com/Articles/How-does-community-property-law-work-in-Texas.shtml
Thanks for your response! In this case, would some sort of election need to be made with the federal MFJ tax return? Or some sort of statement provided?
You would not need to submit anything with the return for the Married Filing Joint classification. However, you will want to maintain record for proving a common law marriage exists.
It is not required to have the common law registered at the county clerk's office but you can file a common law marriage declaration as proof the common law exists.
Another form of proof would be maintaining records for tax years Married Filing Joint was claimed showing joint lease agreements, joint insurance policies, and joint bank accounts.
It is important to maintain a record for any year the status is claimed for documentation in case of an audit.