The Bayern Munich striker revealed the pair played together in Palm Beach, Florida, around 18 months ago. "I played alright to be honest," Kane said. "He invited me to play when I was down in Palm Beach.
"So yeah, when the president invites you somewhere, it was a pretty surreal experience just to meet him and obviously play golf with him. His golf is pretty good, to be honest with you.
"I hope I can play golf as good as him when I'm his age, that's for sure. A unique experience, but I was just grateful that he invited me to play."
Trump, 80, had revealed details of the round earlier in the week, offering his own verdict on Kane both as a golfer and a footballer.
"I think Kane is a great player," Trump said, after Kane scored twice to help England beat Mexico 3-2 in the last 16. "I played golf with him and I like him a lot. He's a good golfer too. He's really great."
Kane has been in outstanding form throughout the tournament, scoring six goals and adding one assist as England chase a first World Cup semi-final appearance since 2018. The United States is co-hosting this year's tournament alongside Canada and Mexico.
England's preparations for the Norway game also included a visit from David Beckham, who attended training at Inter Miami's facilities in Fort Lauderdale on Friday alongside his sons Romeo and Cruz. Kane revealed the former captain, who won 115 caps for England, has stayed in regular contact with the squad throughout the tournament.
"He just wished us luck," Kane said. "After most games, he messages me, and we stay in touch."
Kane said the squad were determined to make Beckham proud as they bid to reach just a third World Cup semi-final in 60 years, with Saturday's game against Erling Haaland's Norway kicking off at 22:00 BST.