Perhaps it's not super proper english, but I have always said "I'm waiting on you" if I'm actually waiting on someone to catch up (in other words having nothing to do with being a waiter). This gave me a wrong answer for that though.
I'm from the south, so it could be a dialect thing.
In english you can say both "I am waiting for you" and "I am waiting on you". The former implies patient waiting what the latter implies impatient waiting. If "jag väntar på dig" means "i am waiting for you", is there any way to imply the nuance of impatience that "I am waiting on you" holds in english?
It's just that we need the preposition with some verbs. So in Russian you don't use a preposition with ждать, (they do in Polish: czekam na ciebie) but you do need one with e.g. думать - думать о тебе. Basically you just have to learn which verbs require a preposition.
It's possible to say väntar without a preposition in some contexts, but it has a different meaning – 'expect' in English: Jag väntar dig klockan fem 'I'm expecting you at five'. I think that's probably also ждать in Russian, but wait means 'be somewhere until someone arrives' whereas expect means 'believe that someone will come', so the meaning is pretty different.