$15-$20/acre should be about right but I have seen some listed in the area for close to $30/acre so the price varies quite a bit and as you can imagine, the price usually corresponds with location, available game, amenities, etc. I have seen some leases listed on the McAllen/Edinburg craigslist so that may be a good start for you. We used to drive around an area we were interested in and stop at the country stores to browse the classifieds for listings or chat with the locals for any leads on leases so you may try that as well. Texas Parks and Wildlife has a link on their site for lease listings across the State and leasehunter.com has several listings as well. Is there a specific reason you are looking at Starr County? If you can find a reasonable deer lease in Willacy County, jump on it. That county is loaded with game.
Edit: Unless you know the owner, I would try to get some kind of contract or documentation of a lease agreement for your own protection. It's not right, but without lease documentation, a landowner can kick you off a lease without warning, reason or consequence.
[This message has been edited by agrc (edited 2/2/2010 9:52p).]