Detective Inspector Stephen McCulloch said the protester breached a no-fly zone over Turnberry hotel and committed a criminal offense.
Greenpeace said the glider carried a banner reading “Trump: Well Below Par” on Friday night to protest his environmental and immigration policies. The group claimed that the protest forced Trump to take cover, with a statement saying “as the glider appears overhead the president can be seen making for the entrance breaking into a trot.”
It said it had informed police about the stunt 10 minutes before the glider arrived.
Thousands of people are expected to join anti-Trump protests across Scotland on Saturday.