I was going to recommend a climbing rose. But most of them have thorns. Unless you go for Zephirine Drouhin rose, which is virtually thornless. However, I don't know how it will fare in your climate. You can check on the rose forums.

There are several fragrant clematis. Clematis Montana, Clematis rubromarginata, Clematis sweet summer love.

Other vines, are Moon flower (Ipomoea alba), and other less fragrant honeysuckle vines. You need to check for the toxicity of some these vines, for children and animals.

Go to the fragrant plants forum and ask for more advice.

Various Jasmines - I don't know which would grow in Texas.

Try gold flame honeysuckle ! It is fragrant and vigorous but non invasive . Still attracts hummingbirds and is very pretty.

I forgot Passiflora.

Here is a link that might be useful: Passiflora Forum

I was going to suggest a passiflora. Star Jasmine is also nice - should grow there - and is evergreen which is a big plus.

I love clematis, but they take forever to establish, I would only plant them in combination with something else because you won't get immediate gratification.