Well, you could just take a metallic wire and run it from the back of your computer to a properly grounded thing.
Traditionally (15+ years ago) you might unscrew a screw at the back a bit and
clamp one end of the wire and rescrew. Then connect the other end to a heating pipe (Something metallic that will go to the ground).
However, your case really should be grounded by way of your PSU.
Your PSU
should be electrically connected to the rest of the case and your PSU
should be connected by a grounded power wire to a proper electric grid.
If your home has ungrouded outlets you may want to use a solution described above or google how to deal with ungrounded outlets in a modern home (as there are other solutions).