If you have an old foundation that does not have rebar, and you are going to tear down the existing house and rebuild. Is there a way to reinforce with rebar in the existing foundation?

What kind of foundation, block, concrete, stone?
Have a structural engineer check the foundation before tear down and after tear down. He/she can tell you what needs to be done if anything to the foundation before re-building.

Check local code requirements, In my area its 25% that is if your rebuild 25% of the structure the entire structure must be brought up to "code", if the home is as old as I'm thinking it is, then its best to just just install a new foundation immediately on the outside of the existing one and its easier to just blast jackhammer the necessary plumbing and accesses thought the old foundation then to try and "finesse" the old foundation back into shape.