If you bump the series up to present day Ranma would most likely use a cell phone but is unlikely to own one. Since pretty much every Japanese teenager has one and that isn't an exaggeration since more than 95% of them have at least one Ranma would borrow (or steal if annoying person like Kuno).
While he doesn't have much need for a cell phone since he is not very communicative (he's pretty secretive and doesn't really have a need to contact people much and would rather some people not be able to contact him) and he often travels to places that wouldn't have a signal (he goes into the wild, abandoned islands, remote villages, and on mountains several times). The main obstacle to him owning one is that they aren't durable enough. It would have to be tough enough to withstand Ryoga's punches, energy blasts (things like ki blasts, air pressure blades, and vacuum blades) extreme temperatures (he has been attacked with flame attacks multiple times and been in freezing temperatures), shock proof (people have used electrical shock weapons/attacks - himself to Mousse, Kodachi multiple times, Rogue the Ashura used lightning), water proof (gets splashed multiple times a day and submersed fairly often), and various other attacks extremes that he himself withstands. Ranma's lifestyle, as it is, simply is not compatible with an item that you carry around with you constantly.