He goes on to brag about how he recruited a teenager with no experience simply because she was attractive.
"A beautiful girl, who was 17 or 18, applied to be a waitress," Trump says in the video.
"So beautiful, she's like a world-class beauty ... and my people came [and] said, 'Mr Trump, she has no experience.'
"So I interviewed her anyway because she was so pretty and I said, 'Let me ask you, do you have any experience?'
"She goes, 'No sir.'
"I said, 'When can you start?'"
For Juliette's part, she appears to be quite flattered by the attention on stage and leans in for a friendly kiss from the real estate titan.
After telling Juliette "you can work on my plane anytime", Trump's gaze lingers as she walks off the stage.
"See now, if she worked on my plane, that's like a death wish for me right?" he says to the guffawing crowd.
"That's like an alcoholic ... you put a scotch in front of him. He's like -" At this point Trump jitters uncontrollably with his mouth agape.
"This would be my form of alcoholism."
The video has been unearthed amid a report that Trump has been hit with a subpoena demanding his campaign hand over all documents pertaining to women alleging he touched them inappropriately.
The lawsuit has been filed by Summer Zevros - a former contestant on Trump's reality TV show The Apprentice - who has alleged the President kissed and grabbed her when she went to his Beverley Hills Hotel bungalow in 2007 to discuss a job.
Speaking to reporters in Washington on Monday afternoon, Trump dismissed the allegations of sexual assault as "fake news".
"All I can say is it's totally fake news - just fake. It's fake, it's made-up stuff. And it's disgraceful what happens," he said.
"That happens in the world of politics."
Trump's campaign for president was almost derailed last year when audio emerged of him bragging about hitting on beautiful women.
"You know, I'm automatically attracted to beautiful - I just start kissing them. It's like a magnet. Just kiss. I don't even wait. And when you're a star, they let you do it. You can do anything," he says on the 2005 recording.
"Grab 'em by the pussy. You can do anything."
