Copied and pasted from the Texas Admissions website:
You may submit as many score reports as you like. If you submit more than one, we will consider the score from the single test date that will benefit you the most. We will not, however, “superscore,” or combine scores from different test dates (a critical reading score from one test date with a mathematics score from another test date, for example).
We strongly encourage you to send us the results from all tests you take.
So taking the SAT or ACT again can only help and not hurt your application.
Here’ where I found this info:
http://admissions.utexas.edu/apply/freshman-admission#fndtn-t33-multiple-score-reports