The Hollywood actor received a rock star welcome during the event at Cineramageddon - a drive-in cinema situated on the Somerset site.
He introduced his 2004 film The Libertine along with film director Julien Temple but began talking about religion and President Trump following questions from the 1,500-strong audience.
"I think he needs help and there are a lot of wonderful dark, dark places he could go," Depp said, to cheers from the crowd.
"It is just a question - I'm not insinuating anything.
"By the way, this is going to be in the press. It will be horrible.
"I like that you are all a part of it.
"When was the last time an actor assassinated a president?
"I want to qualify, I am not an actor. I lie for a living.
"However, it has been a while and maybe it is time."
Depp, who arrived in a blue vintage Cadillac, was greeted with crowds of screaming fans holding phones.
He smoked a cigarette as he posed for pictures and jumped on the car bonnet without prompting. Wearing a black shirt and distressed jeans, he also sported a black hat with a silver ribbon around it.
Introducing the film, he said: "Thank you so much for having me here.
"This is beautiful, chaotic, madness.
"I made this film, The Libertine - people talk about Lavie of love and all that stuff.
"I made the film because I wanted to try to bring to England a great poet that that missed.
"They missed him because he was written off as a jokester, a hoaxer.
"This guy is one of the deepest poets. He was very religious.
"Someone asks to talk about religion. How long you got?
"It is a film that a lot of people worked very hard on."
Fans, many sat in vintage cars and trucks, then enjoyed a screening of The Libertine.