The answer, in my opinion, is probably yes. It is customary for landlords to make repairs to homes that they lease. The Texas Property Code also cites that tenants can make demand of their landlords to repair issues that may materially affect the health or safety of any occupant.
In this case, if you have a rat infestation, I would recommend sending a formal written request to your landlord by Certified Mail and giving him a timeline to repair the issue. Since the Property Code allows you to make this demand, then (if not action is taken by the landlord) make the repairs yourself and deduct it from the rent, you may consider that course of action.
That said BE CAUTIOUS the Property Code has some specific requirements about the demand letter, the timeframe and what you can do. I would recommend speaking to a lawyer to get some help with this. I am in the Dallas area so if I may be of help please feel free to contact me.