Short answer, yes, though in Texas a handgun has to be concealed. But I’ll tell you a true story by way of illustration. 
Grandma LSP was driving with Great Grandma LSP, in Plainview, West Texas, during the ’20s oil boom. They were wild times and an outlaw figured he could rob the two women. He thought differently when Great Grandma LSP produced a revolver from the glove box.
Plainview in the 1880s?
That was the ’20s and this is now. Have we become more, or less lawful since then?  And if you’re carjacked by Justin Welby, or some other bad actor, would you be more, or less safe if you’re armed? The NWO libs insist that you’ll be safer if you aren’t and that the police will protect you.

That wouldn’t have worked for those two women in Plainview in the ’20s and guess what, it wouldn’t work now. And I’ll go further than that and say that one of the hallmarks of a free society is the ability of its citizens to defend themselves.

Go ahead and say otherwise, but know that not only are you on the side of Hillary Clinton, the NYT and “Huffpo,” but also Hitler.
Gun rights.