While the specifications state (on Best Buy's site) that it comes with a PCI-Ex1 slot, I have no idea where it is or how you'd connect a graphics card to it. Best guess would say, you can't install a card in that system.
*EDIT* i may have to change my advice, I have not been able to find any internal pics or other information about adding a graphic card to this ASUS. You will have to open the case and look to see if there is a way a graphic card can be installed and accessed from the back panel. There may not be room or it may be configured in a way that it is not an option.
There are several cards that will work. You need a low profile or low profile "ready" graphic card. Your system uses a G35 motherboard so it will use any PCIeX16 1.0 or 2.0 low profile card. What are you planning on doing with the system ? (gaming, HTPC, general computing and light gaming?) What is the resolution of your monitor ? (example is a 19 inch LCD at 1440X900) What power supply does your system have in it ? (example is a 250watt with 17 amps on the 12V ) Much depends on what card you can install on what power supply your system has in it. If you have a 300w power supply, then this card would be a decent solution without more info.