Son of Mungo Maxwell. Married to Margaret Maclellan of Barscobe, a niece of Lord Kirkcudbright.
He was sent to France at age 7, brought up as a strict Catholic, was educated at the R.C. College in Douai and was a soldier in one of the french regiments which landed in Scotland in 1745 to support the Jacobite rebellion. Later on he converted back to protestantism, and won a lawsuit concerning the estates of his cousin Sir Thomas Maxwell, the 6th Baronet of Orchardtoun, in 1761.
Like many others in the same circles, Robert Maxwell lost the larger part of his fortune as a result of the failing of the Bank of Ayr in 1773.
Maxwell arrived at Kirroughtrie (Patrick Heron's estate), where Boswell was staying at the time, together with Lord Kames on September 22, 1762. Boswell described him as "a good, honest, plain man, by no means destitute either of natural sagacity or of knowledge." On October 4 of that same year, Boswell spent the night at Maxwell's estate at Gelston.