Water is covalent, not ionic. OK, it does fall apart into ions, but only to a tiny tiny extent. As in, one molecule per 100,000,000,000,000 molecules of water falls apart into H+ and HO-. Essentially any ions would come from outside sources.
Electrolysis of water is real but it relies on those extraneous ions to carry the charge through the liquid. No ions, no transport of charge.
I can ionize water in my kitchen. Glass of water. Salt shaker with salt. Add salt to water. Voila!