That Thinkcentre has a 2nd-generation Core i5 2500 processor, so it has version 2.0 PCI-E x16 slot, which is compatible with any PCI-E x16 graphics card on the market. However the power supply isn't very strong.
According to the specs on Tiger Direct that computer has a 280 watt power supply. While that's better than 220 watts, it's still only enough to support low-end graphics cards like a Radeon HD 6450 or GeForce GT 610. Those are $50 models which are just slightly better than your integrated graphics.
You'd want to upgraade the power supply in order to install cards with decent gaming performance.
For example, this PSU:
http://www.newegg.com/...6817182074
Can support entry-level gaming cards like the Radeon HD 7750.
http://www.newegg.com/...6814102969
While this PSU:
http://www.newegg.com/...6817139027
Can support cards up to the $220 level, like the GeForce GTX 650 Ti/GTX 660 and Radeon HD 7850/HD 7870.