Green’s Dictionary of Slang

giggy n.

the anus.

1958

T. Berger Crazy in Berlin 187: You can keep all the rest and stick them up your giggy.

In exclamations

up your giggy! (also up your gig! ...gigi!)

(US) a general excl. of contempt, dismissal.

1953		W. Eyster Far from the Customary Skies 17: Aw, up your giggy with a wire brush.
1955		F. Brookhouser Now I Lay Me Down 65: Ah up your giggy.
1968		G. Legman Rationale of the Dirty Joke (1972) I 156: The hand-gesture is still very much alive [...] often accompanied with the spoken catchphrases [...] ‘Up your ass!’ ‘Up your gig!’ ‘Up your poop-a-doop!’ ‘Up your fur-lined shit-shoot!’ and the like.
1977		Maledicta 1 (Summer) 15: Nowadays a person may be told to stick it or stuff it [...] This is essentially an unfriendly remark, and may be answered with: up your gigi, or up your fur-lined shit-chute, or just up yours — and give it a left-hand turn.