The 26-year-old Glendronach single malt whisky was bottled in 2012 to mark the opening of Trump International Golf Links in Aberdeenshire.
Experts believe the lot will go for a four-figure sum, with an estimate of £2,500 on the bottle.
It is being sold at McTear's Auctioneers in Glasgow on 13 January.
McTear's whisky expert Laurie Black said: "I suspect Mr Trump's imminent elevation to the position of 'leader of the free world' will have a significant bearing on the value of the 26-year-old GlenDronach, but the fact remains that this is also a quite stunning whisky in its own right."
The sale features in McTear's rare and collectable whisky auction, which also includes a cask of 43-year-old whisky from the closed North of Scotland Distillery for £50,000 and a bottle of 52-year-old Macallan 1950 that could fetch in excess of £9,000.
A rare bottle of whisky signed by Donald Trump is going up for sale in Scotland a week before before his inauguration as US president.