So you have ASRock A88M G3.1 Board you can find all the details about your motherboard here http://www.asrock.com/mb/AMD/A88M-G3.1/
Now the question is resolved when you ask if you can run graphics card on your system if it has onboard graphics. Yes you definitely can as you have got PCI ex Slot on your motherboard.
But just having a pci ex slot doesn't mean you can run graphics card right away... the main component you require is the psu or power supply for powering the card. You need to tell which psu you're using, how much watts of power it can deliver.
Open the case and look for branding on the psu. Your PSU may or may not would look like this, but it will be similar.
Look for the watts, it would say 400 or 450 or 500 or 550 or 600 and so on.... Depending on this value you can choose the card that would be able to run with your current PSU. But i would say, anything above 550W from a good brand and you can pretty much power any card... But lets not get to that right now.