From scholion on Aristophanes Clouds 133 (link 2 to Aristophanes below). Expressions similar to this are common in comedy; see LSJ on korax "raven" (link 1 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 ἐς κόρακας (Epsilon 3154).
[1] This additional sentence, not in the equivalent entry in Zonaras, is a possible reference to LXX Proverbs 24.52 (30.17).