American Airlines may want to pay for an exorcist to fly on each of its flights ... 'cause one passenger claims her brother was fighting off evil demons -- and allegedly ended up whaling on some poor crew members.

Here's the deal ... a 31-year-old man named Delange Augustin boarded a flight in Savannah, Georgia bound for Miami, Florida earlier this week with his sister Medjina -- and, the plane took off without incident carrying the siblings, six other passengers, and five crew members.

According to FBI documents, just a minute after takeoff, one of the flight attendants says they noticed Augustin was stomping, yelling incoherently, and appeared "to be in a fit of epilepsy."

Flight attendants ran to his aid ... but, Delange allegedly kicked one of them in the chest, on purpose, sending her across a row of seats and into a window. Delange is said to have continued kicking and punching the seat and the passenger in front of him while the plane returned to the airport gate.

While deboarding, crew members say Augustin -- holding his sister tightly -- rushed at one of them and allegedly started throwing "haymakers" at her before other passengers wrestled him to the ground.

Augustin was taken to a hospital for evaluation -- and for swallowing a set of rosary beads ... though he was eventually discharged from the hospital, arrested for interference with flight crew members, and booked at Chatham County Jail.

Officials spoke with Medjina ... who claims she and Delange were traveling to Haiti to "flee religious attacks of a spiritual nature."

Medjina -- who says she can "feel the spiritual fight, but cannot see" -- says Delange told her to close her eyes and pray because "Satan's disciple(s) had followed them onto the plane and the legion did not want the Augustins to make it to Haiti."

As for the rosary beads ... Medjina says they are a source of strength in spiritual warfare -- and, he decided he needed that strength inside him.