From a scholion on Aristophanes, Clouds 133 (web address 1 below). Expressions similar to this are common in comedy; see LSJ on korax "raven" (web address 2 below). Probably they derive from the carrion-eating reputation of ravens and crows. Other ideas about the origin of the phrase, however, are gathered in the entry e)s ko/rakas (epsilon 3154).
[1] This additional sentence, not in the equivalent entry in ps.-Zonaras, is ambiguous. Perhaps [CR] a reference to Proverbs 24.52 (30.17) LXX; alternatively [DW] to epsilon 3154 (above).