According to the Transgender Law Center's State-by-State Overview: Rules for Changing Gender Markers on Birth Certificates:
[Texas] law does not explicitly provide for gender marker correction. It may be possible with a doctor’s letter and/or a court-ordered gender change, but historically has been difficult to acquire.
Even though the law does not say exactly how to change the gender marker on your birth certificate, we have compiled information below to guide you through the process. You will also find information to change the gender marker on other identity documents.
An important step in changing your identifying documents to accurately reflect your gender is to get a court order. There is not an "official" form to ask the court for an order changing your gender marker, but Texas attorneys have developed sample forms you may be able to use.
If you only want to change your name, please see our guide to Name Changes in Texas.
If you need help filling out forms for a gender marker change, there are some groups you can contact:
Once you have a court order to change your name and/or gender marker, you will need to change your identifying documents. Common documents and how to update them are listed below.
Texas Birth Certificate
Texas Driver's License
United States Passport