Cards do not proc off themselves. Ceris is correct. You would have to have another Starving Buzzard in play and that would cause you to draw another card when it is played.
"A minion has to be in play already for its ability to be active. So a minion ability that requires you to meet a specific condition, such as playing another beast with Starving Buzzard or an ability produced by a Battlecry minion, cannot target itself."