This is the spec sheet for the Optiplex GX280: Documentation
It says you can use a PCI-Express graphics card (note, this is not the same as the slower PCI), but it will need to be a 'low-profile' card to fit in the small form-factor case. This will limit your choice of cards to the smaller, less powerful ones.
Something like a GeForce GT430
or Radeon HD5450
would be suitable.
You will probably also need to replace the Power Supply Unit (PSU) which might not be strong enough to cope with the extra power requirements of a PCI-E card. Remove the side panel from your case so you can see the label on the side of the PSU. Please post back with the details from the label (make, model, total watts, +12V amps).
You can install up to 4gb RAM if you haven't already, but 2gb should be plenty.
Your CPU is a P4 which will struggle with most modern games, but should be ok for older games like NFS Carbon and CoD.