The plane's erratic turn was visible on the flight tracking website Flight Aware. It landed safely at Leonardo da Vinci Rome Fiumicino Airport at 4:21 local time.
There were 199 passengers on board and 15 crew members, the airline said. They were taken by bus to a terminal at the airport and screened by security personnel.
The flight was a Boeing 787 Dreamliner, capable of carrying 296 passengers, according to Boeing.
Officials reported a bomb threat was received via email, prompting the diversion. But the threat was later determined to be unfounded, according to ABC News.
"Safety and security are our top priorities and we thank our customers for their understanding," American Airlines said in its statement.
Indian authorities insisted the aircraft be checked out before landing at Indira Gandhi International Airport in Delhi, officials told ABC.