Is this spider poisonous
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.
Your spider appears to be one of the orb-weaver spiders of which there many species. Orb weaver spiders, also referred to as writing spiders, are the most common group of builders of spiral wheel-shaped webs often found in gardens, fields and forests. Sometimes it looks like they write something in the middle of the web when they join the center together, thus term "writing spiders."
Here is are a couple of publications on spiders for your general information: