Events from the year 1768 in Scotland.

• Lord Advocate – James Montgomery
• Solicitor General for Scotland – Henry Dundas

• Lord President of the Court of Session – Lord Arniston, the younger
• Lord Justice General – Duke of Queensberry
• Lord Justice Clerk – Lord Barskimming

• 10 June – construction of Forth and Clyde Canal begins (Act 8 March).
• 10 December – first volumes of Encyclopædia Britannica begin publication in Edinburgh.
• Bridge over River Deveron between Banff and Macduff swept away in flood.
• David Dale begins his own business importing linen yarn from the Dutch Republic to Glasgow.
• Duchal House extended.
• Alloa Waggonway open.

• 2 May – Zachary Macaulay, abolitionist and statistician (died 1838 in London)
• 3 May – Charles Tennant, chemist and industrialist (died 1838)
• 9 May – James Thomson, Presbyterian minister and editor of Encyclopædia Britannica (died 1855 in London)
• 11 May – David Hamilton, Glasgow architect (died 1843)
• 14 July – James Haldane, soldier and evangelist (died 1851)
• 29 August (bapt.) – William Erskine, Lord Kinneder, scholar and songwriter (died 1822)
• 23 September – William Wallace, mathematician (died 1843)
• 6 November – James Hay Beattie, poet (died 1790)
• 10 November – Thomas Thomson, advocate, antiquarian and archivist (died 1852)

• 15 June – James Short, mathematician and optician (born 1710)
• 1 October – Robert Simson, mathematician (born 1687)
• 12 October – James Douglas, 14th Earl of Morton, astronomer (born 1702)