The uploader said the apparatus measures more than 26 inches from the muzzle of the gun to the rear of the frame.
The FAA said it is investigating the video to determine whether any laws were violated.
"The FAA will investigate the operation of an unmanned aircraft system in a Connecticut park to determine if any federal aviation regulations were violated. The FAA will also work with its law enforcement partners to determine if there were any violations of criminal statutes," an FAA spokesman told CNET.
"We currently have rules in the books that deal with releasing anything from an aircraft, period. Those rules are in place and that would prohibit weapons from being installed on a civil aircraft."