If you already have the graphics card, you should be able to tell really quick.
Yes, the g31 TM-P35 has 1 PCI-E 16x GPU slow in it. So it's compatible. The real question is whether the GPU will fit in your case (I think it's 10.5" long) and if your Power Supply has the right PCI-E power connectors and enough power output.
Here's the specs page for your motherboard, which I found faster than you typed in your question.