"origin unknown", but here's what OED has, fwiw:

[mod.Fr.; orig. unknown. According to Litt. first used in 18th c.; referred by some to Gr. {alenis}{mu}{phi}{giacu} about + {gamma}{gufrown}{rho}{omicron}{fsigma} circle, or -{alenis}{gamma}{omicron}{rho}{giacu}{alpha} speech, cf. allegory, category.]

(sorry about the Greek; that's the way it copies)

usu. spelled amphigory in Eng.