Wow!! That must be a dress patch from a very short era. A good friend and protege of mine is now a Trooper. I've contacted him and asked him to check into it. Hopefully I'll have you a little info soon.
I do know that the long standing motto of the Texas DPS is "Courtesy, Service, Protection" and I don't see that on the patch. Hopefully my buddy can give me a little more info on it.
Just texted a pic of it to my bro who has been a Trooper for almost 10 years and is friends with several Rangers. It was never an issued item. The Rangers have never had a uniform, and any patches that would have ever been official would have had green leaves on either side, as that is the way it has been throughout the history of the Texas DPS. Sorry for the bad news, but is is very cool. Please don't take what I say as gospel, but I'm almost certain it is. I'd do a little more digging if I were you.... you may uncover some cool bits of info.
AJ