The 31-year-old, who is known for posting the thoughts of famous philosophers such as Friedrich Nietzsche on Twitter, is believed to be studying for the degree at Roehampton University.
Barton tweeted on Thursday: "Off to my first lecture this afternoon. Eyes peeled, ears open, brain engaged..."
According to the Daily Mail, Barton was inspired to take on the course following the death of the co-founder of the Sporting Chance clinic Peter Kay.
Kay helped treat Barton through his issues during the early years of his career.