Lots of rugby gets played in Dallas and the burbs Little Buddy. Just look around.
I know several guys that play.
I think there's some groups on Facebook for it.
Try your municipality's parks and rec department. They almost certainly manage the leagues, or at least know who the contacts are, as they would probably manage the facilities access. As well, if you're in college, your student services office likely has some information on leagues.
I took the time to type "dallas ruby" into google for you, and got this back:http://dallasrugby.org/http://www.darc-rugby.com/http://www.quins.com/http://www.dallasdiablos.org/Dallas_Diablos_RFC/Home.html
The Texas Rugby Union, which I found in Google for you, is the sanctioning body for Texas. Almost certainly they'll be able to help you, as well:http://www.texasrugbyunion.com
I reckon that will get you headed the right direction. There are many additional links in the google search results. You might wish to give it a try for yourself.
Google is a great tool, and very simple to use.