What is this ?
Your spider appears to be a common house spider but because I cannot enlarge the picture without losing a lot of the resolution I cannot properly identify.
All spiders are venomous, and they may bite when harassed or provoked but it is no worse or harmful than a bite or a sting from other insects. Fortunately, most spiders have to really be provoked into biting. The only spiders that are considered "dangerous" in Texas are the Black Widow spider and the Brown Recluse spider. Your spider is neither of these.
Here are a couple of publications on spiders for your general information: