Son of Patrick Craufurd of Drumsoy (d. 1733) and Jane Craufurd, 2nd daughter of Archibald Craufurd, 15th of Auchenames. Married twice, firstly to Elizabeth Middleton (d. 1746) and secondly (in 1750) to Sarah, daughter of Hugh, 12th Lord Sempil.
Craufurd was twice elected MP for Edinburgh (1741 and 1747), and later, in 1761, for Renfrewshire.
On January 9, 1763, in London, Boswell was received "with uncommon kindness" by Craufurd, who had heard that Boswell was looking for a commission in the guards. Craufurd told Boswell that he knew Lord Rothes well and that he would introduce Boswell to him, which he probably never did. Boswell described Craufurd as a "very honest and very generous man [who] saved Lord Rothe's estate by advancing a large sum of money."