Is that your main electrical panels grounding rod? If so the wire is woefully under sized. It's been a long time but I seem to remember having to use a #6 bare copper wire to attach to the ground rod. It also needs to be protected in a conduit.

I would certainly advise hiring an electrician. Being that it's old you may be able to not have to put in the current ground rod requirements. This requires several ground rods spread apart and a continuous conductor between them terminating in the panels ground bus. It also specifies that it needs to be protected in a conduit. If you must bring it up to code rather than just fix it up to what the code was at the time or then it will cost a good bit of money.

I would strongly recommend that you DON'T mess with this. Grounds are there for your protection in the event that a current carrying conductor comes in contact with a metallic part of a box, fixture or appliance and shorts to ground rather than be a potential shock hazard to you.