By "political scientist", I assume that you mean an academic researching and teaching about politics. A path to that sort of career might involve studying politics, on its own or as part of a mixed degree such as PPE, HSPS, history and politics and the like at places such as the LSE, UCL, Oxford, Cambridge etc. You'd then need to move on to a Masters and a Doctorate in order to compete for a full time academic post.
Or you could seek a job in the civil service, or as a SPAD, in lobbying, think tanking, journalism, and so on.
You could qualify as a barrister with a degree in any subject followed by a PGDL, the Bar course, and a pupillage but obtaining a pupillage is not easy (approximately 3000 people chase 650 pupillages each year).