Both his parents were associated with the Church, with his father being the minister of Arbuthnott and his mother being the daughter of the minister of Farnell and dean of Brechin. Alexander Arbuthnott was well educated having studied at Marischal College, Aberdeen.
Pareho ang kanyang mga magulang ay iniuugnay sa Iglesia, sa kanyang ama na ang mga ministro ng Arbuthnott at sa kanyang pagiging ina ang anak na babae ng mga ministro ng Farnell at dekano ng Brechin. Alexander Arbuthnott ay well-aralan sa pagkakaroon ng aral at Marischal College, Aberdeen.