I'm assuming when you say "old wire with only the hot and neutral" you mean a cable with only a hot and neutral wire. The answer then is no, you can not run a separate ground wire. It must be part of the cable assembly.

If you happen to have metal conduit, the conduit itself functions as the ground and there would be no need for a separate ground wire in most circumstances.

Look in the switch box to see if there is newer cabling feeding the switch, with just the old cable going from the switch to the light. If that's the case, then it may be fairly easy to replace the cable feeding the light.
If the whole circuit is still old wiring, it may be more difficult.

Thanks for the fast responses! Unfortunately, the cable feeding the switch is old as well. I considered adding an entirely new circuit to supply my new lights but my main problem is i cannot access the old cables that i would be abondoning. If I abandon the current setup...im assuming i would just have to terminate the cable in the attic in a junction box...not a big deal. But i would also have to put a cover plate over the existing wall switch? Im not thrilled about that idea. And if i ran new romex i could not feed the new cable to a place that is relatively close to the old switch which is important to my wife. Guess, that is why i was hoping to somehow just ground the existing set up.

If you disconnect the whole circuit from the breaker box, then the wiring can be abandoned and no longer has to be accessible. If wiring doesn't have electricity moving through it (or the potential to have electricity moving through it) then it is just pieces of metal and plastic in your walls. No codes apply. You can remove the junction box and patch over the drywall.
When you disconnect the circuit from the breaker box, cut the wires back far enough so that they can't be re-connected. Maybe even leave a note on the end of it that the wiring is abandoned and can no longer be used, so that some future owner won't stupidly try to hook it back up.

I'm curious, if you can run a bare copper wire from
your breaker box, to the fixture, then why can't
you run a proper cable?

And if i ran new romex i could not feed the new cable to a place that is relatively close to the old switch

If you could run new cable from the breaker box to the location of the light, then you could use the old ungrounded wire from the light to the switch as a switch-loop. That way at least your light would be grounded even though your switch box wouldn't be.
Then, if you abandoned the old circuit (ie. disconnect from breaker box), you'd just push the unused (and unenergized) cable out of the switch's box.
Or if you didn't abandon the old circuit, you'd just put wire caps on the old feed in the switch's box and push the wires out of the way into the back of the box.