After attending Sheffield Grammar School and Dr. Philip Doddridge's academy at Northampton, Roebuck studied medicine at Edinburgh, where he developed a taste for chemistry from the lectures of William Cullen and Joseph Black.
Efter at have gået på Sheffield Grammar School og Dr. Philip Doddridges akademi i Northampton, studerede Roebuck medicin i Edinburgh, hvor han udviklede en interesse for kemi ved at følge forelæsninger af William Cullen og Joseph Black.