That is one of the many orb-weaver spiders species found in Texas. I have attached article on the Black and Yellow orb-weaver which is one of the largest.
Orb-weavers have very flat and sometimes elaborate webs that they use to catch prey. Normally they will position themselves in the middle of the web.
You can also conduct a Google search on Orb-weaver spiders in Texas to see how varied the species is. The very flat web that stretches between tree limbs, between trees or across a window on a house is very common of these various species.