In a CRT monitor, you have a ray of electrons that travel in vaccum and it is electricity outside wires. With a similar device, you can create a ray of protons and have also electricity with protons instead of electrons.

Another posibility is to use a water solution with acid. A part of the electricity is made of H+ that are just protons. (Actually, each proton is atached to a water molecule, so it's more like H2O+ than a plain H+.)

I'm triying to imagine a wire where protons can move. I don't think it's theoreticaly impossible, but they are mmuch heavier and bigger than electrons, so they it looks very difficult to find a material where they can move freely.