I don't know much when it comes to electrical engineering (and especially how the human body would function as an antenna) but if such a thing were to exist, you'd likely need a thin wire either implanted in your head or hanging outside your skull. Maybe a whip/telescoping antenna if you really wanted to look like a jackass.
AM would be a lot easier though, at least in theory. AM radios don't need a long external antenna since they use a small built-in ferrite bar with copper wrapped around it instead. AM is fucking terrible though, it's usually not good enough for music (only voice) and your cell phone would very likely cause interference.
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