You need a fishing license.
https://tpwd.texas.gov/regulations/outdoor-annual/fishing/general-rules-regulations/general-fishing-regulationsFishing License Requirements
Any person who takes or attempts to take fish, mussels, clams,
crayfish or other aquatic life in the public waters of Texas must have a current Texas fishing license with the appropriate endorsement. A saltwater endorsement is required to fish in coastal waters; a freshwater endorsement is required for inland waters.
The regulations do not specifically mention a crawfish trap. They do mention a minnow trap:
Minnow Trap
May be used to take NONGAME fish only.
Trap may not exceed 24 inches in length. The throat may not exceed 1 inch by 3 inches.
Gear tag valid for only 10 days must be visibly attached.
That should cover a crawfish trap.
Of course, the state does not know how to spell crawfish!