Most anti-static mats have an anchoring point (metal snap) to connect the wrist strap to and a second one to tie to earth ground. If you have a clip type of cord on your wrist strap you can clip it to the mat and then using a clip or snap connection from the mat to earth ground.
As others have stated your 3 prong outlets offer a good ground point. I would recommend making sure you don't have any mis-wired outlets in the area your working (black wire going to the chrome screw on the side of the outlet - needs to be to the brass colored screw!)