Cops radioed air-traffic controllers at JFK and ordered them to reroute a taxiing Panama-bound plane to an emergency area yesterday — all for a stolen cellphone, sources said.

Airport custodian Raeshawn Gibson, 24, of The Bronx reported her iPhone 4S stolen after she stashed it in a bathroom paper-towel dispenser, said law-enforcement sources. Staffers aren’t allowed to use their phones while on duty.

Luzmila Coffre Castillo, a Panamanian who was about to board the flight, allegedly saw Gibson hide the phone and snatched it, sources said.

The janitor alerted cops to the theft at around 9 a.m., sources said.

Port Authority Police Officer Regina Womack used a phone-finder app to trace the device to a taxiing plane as it was about to depart.

PA Police Sgt. Bernard Buckner then radioed the control tower and asked that the Copa Airlines flight be rerouted to a secure police gate.

The cops boarded the packed plane and traced the phone’s “ping” to Castillo’s seat.

Castillo allegedly confessed and was arrested, sources said.