Francis Scott, Earl of Dalkeith (19 February 1721 – 1 April 1750) was a Scottish nobleman.
He was the eldest child of Francis Scott, Earl of Dalkeith by his wife Jane, daughter of James Douglas, 2nd Duke of Queensberry. In 1732 his father succeeded as second Duke of Buccleuch and Francis assumed the courtesy title Earl of Dalkeith. He was educated at Christ Church, Oxford, and was awarded the degree of Master of Arts on 26 January 1741.
On 2 October 1742 he was married to Lady Caroline Campbell (born 17 November 1717), eldest daughter and co-heiress of John Campbell, 2nd Duke of Argyll and 1st Duke of Greenwich. They had four sons and two daughters:
Lord Dalkeith was elected to Parliament as Whig Member of Parliament for Boroughbridge in a by-election on 22 April 1746. On 1 April 1750 he died of smallpox aged 29, and was buried at Dalkeith Palace.
In 1755 his widow was remarried to Charles Townshend, later Chancellor of the Exchequer, by whom she had further issue. She was created Baroness Greenwich in her own right in 1767, and died on 11 January 1794. Her title had been limited to her descendants from her second marriage, and became extinct on her death.