Alexander Boswell (1706-1782), lord of Auchinleck, was a judge of the supreme courts of Scotland. He was the father of the author and biographer James Boswell.

Most noted for rescuing of the Auchinleck Manuscript 1740 from a professor of Aberdeen University who was in the process of destroying it. He donated the manuscript to the Advocates' Library in Edinburgh.

Note that also Alexander Boswell's grandson was called Alexander Boswell.