How do you become a sociobiologist?

A good place to begin is to read Edward O. Wilson's book "Sociobiology, The New Synthesis" published in 1975. Wilson is the father of sociobiology: the impact that our genetic inheritance has on our behaviors.

Second, sociobiology is an off-shoot of the study of evolutionary Biology, so understanding the origins of life on earth and the mechanics by which evolution takes place is important. For this, I recommend going straight to the books authored by Charles Darwin - not interpretations of his work.

These two scholars will offer you a good start - and from there it is a matter of finding a university which offers such a degree.