If you have Mobile Insurance on your phone, you'll be able to get a replacement for a deductible of $199.99. If you didn't have the insurance, you may be eligible for an early upgrade for $250 + the subsidized price of the device.
If it's just the screen that's damaged, there are repair shops that specialize in repairing them, so I suggest doing a quick Google search for one in your area. It would most likely be cheaper to do that rather than get a brand new S4.
There's also the eBay/Amazon option of getting a refurbished device at a decent price... just make sure it's an AT&T phone.
*I am an AT&T employee and the postings on this site are my own and don't necessarily represent AT&T's position, strategies or opinions.