Get in the question means derive, of course. But welcome to the question anyway.
Unusually, it appears that the adjective arrived first and raunch is a back-formation from raunchy.
However, ODO says
1930s: of unknown origin.
and OED isn't a great deal more forthcoming
Etymology: Origin unknown.
Perhaps compare English regional (west midland and south-western) raunch to eat greedily, devour, to tear up, to snatch greedily, and also the related adjective raunch (of vegetables) green, uncooked (see Eng. Dial. Dict. at raunch v. and adj.).
In early use frequently in U.S. military aviation.
Their earliest citation is from a 1937 novel, I wanted Wings, apparently published in New York — which may justify "U.S. military aviation", but seems hardly likely to involve English regional dialects. And its usage there,
You're gigged, Mister. Raunchy shoeshine. Raunchy brass. Raunchy haircut. Raunchy shave.
might be related to an early definition, "Inept, slipshod, slovenly; esp. unkempt, shabby, dirty," [OED] but that shifted fairly quickly to its current meaning, " Energetically earthy and unrefined; sexually explicit or provocative; lewd, bawdy, suggestive" [OED, 1943 citation].
So where does raunchy come from? I had thought it might be vaguely onomatopoeic, like pwhoar!, but that sexually-charged usage appears to be derived from the earlier "slovenly", which isn't so far from "sluttish".
Raunchy certainly isn't slang now, although I suppose it may have been between the Wars. But even slang has some sort of cultural reference to create it. What was it for raunchy?