Can I replace the router att gave me with our uverse internet service?

I don't want to keep having to pay 10 bucks a month just to rent a router when I could just go out and buy one. The only issue I see is that their router connects to a phone line. Any suggestions or help is appreciated.|||Their router is actually a modem. A router plugs into the modem. If it's a combo hardware you might be able to call and get a regular modem then put w/e router on it you want