Give me your tired, your poor, your smuggled masses.

New York City’s Immigration and Customs Enforcement (ICE) office is “fully booked through October 2032” for appointments to process migrants released at the southern border, according to an official document exclusively reviewed by The Post — making the Big Apple the ideal destination for migrants with dubious asylum claims and causing a massive headache for those with valid ones.

The backlog means migrants may have to wait almost a decade just to enter the immigration court process — which is beset by further delays stretching out years, sources said.