It is from this act of scavenging for cigarettes and the fact that the only trace they ever leave behind are cigarette butts that they are given their title.
Person 1: Hey bro can I bum one of those? I'll give you one tomorrow after I go to the store.
Person 2: Dude this is like the 5th time you've said that tonight.
Person 1: Come on I'll buy you a drink later.
Person 2: Just take it you damn butt vulture.