What do you define running? If that means you want to achieve constant 60fps then you will have a real hard time, you could probably get around 25 - 30 for $600, the engine of the game is truly bad. You would have to invest more in a CPU then you would a GPU. Here is a build i made that you help you achieve around 30 frames.
CPU: AMD FX-8350 4.0GHz 8-Core $139.99
Motherboard: Gigabyte GA-78LMT-USB3 Micro ATX AM3+ $44.99
Memory: Crucial Ballistix Sport 8GB (2 x 4GB) DDR3-1600 $63.99
Storage: Western Digital RE2-GP 1TB 3.5" 7200RPM $78.68
Video Card : Asus Radeon R9 270X 2GB DirectCU II $149.99
Case: Fractal Design Define Mini MicroATX Mini Tower $85.43
Power Supply: Corsair 500W ATX12V $44.99
Total: $608.06
https://pcpartpicker.com/user/sadlahh/saved/#savedbuild_1720805
That does not include an OS, so you could probably cut down on the case, and storage, up to you.