The 26-year-old Glendronach single malt whisky was bottled in 2012 to mark the opening of Trump International Golf Links in Aberdeenshire and its presentation box was signed by Mr Trump when he visited the course.
The lot, which includes authentication papers, was put up by an anonymous seller at McTear’s Auctioneers in Glasgow a week before the inauguration of Mr Trump as president.
The limited edition whisky was distilled in 1985 and is one of only 504 bottles.
Other memorabilia with Mr Trump’s signature, including books, caps, dollars and presidential campaign signs, are on sale online for hundreds of pounds.
McTear’s whisky expert Laurie Black said it was sold to a Canadian buyer for £6,000 following “intense online, phone and in-room bidding”.
Mr Black said: “There was a huge amount of interest in the bottle and we were delighted with the final price, which was several times more than previous Trump bottles have sold for.
“The Glendronach is a stunning whisky in its own right, however the Trump connection gave this particular bottle a presidential boost.”
The sale featured in McTear’s rare and collectable whisky auction where a bottle of 52-year-old Macallan 1950 fetched £10,000 while rare examples of Springbank single malt went for the same amount.
Mr Black added: “It was a fantastic sale with some truly outstanding whiskies.
“The prices achieved on the day reinforce the view that rare and collectable whisky continues to be a strong investment opportunity.”
The management of Mr Trump’s businesses, including golf courses in Aberdeenshire and Turnberry, is passing to his sons Eric and Donald Jr as he prepares to take office as President.