Well, I would never say, "Phone to me", that's for sure; "phone me", sometimes, but more often, "call me". I do more often say, "Write to me", but if I'm in a hurry for some reason, I'll say, "write me".

I guess for both, it's one of those instances where the preposition (in this case "to", a direction-giving preposition) is implied. Here's a quote from the Interlink Language Center: Prepositional phrases are like idioms and are best learned through listening to and reading as much as possible. You know how, especially when speaking/writing casually, you'll say, for example, "Got a minute?" The implied subject of that interrogative is "you": properly, it would read, "Do you have a minute?" The same principle goes for phone me, I reckon.

Most of the time, I write to someone, but sometimes, lovely maverick, I'll write you.