He probably didn't have one, as we understand the term. The idea of attaching a specific tartan to a particular surname or clan name developed very very late, maybe in the late 18th century, maybe in the 19th, and it may at that have been an outgrowth of assigning specific tartans to particular Scottish *regiments* (e.g. the Black Watch).
Additionally, he seems to have been a Lowlander, and Lowlanders weren't all that big on tartans, kilts, or anything like that until Sir Walter Scott got the idea of "Scottish pride" up and running with his novels.