Well, there's politics, of course. Managing a campaign or working on a campaign team. Writing speeches for a political candidate. Or even running for office yourself. You don't necessarily need a political science degree but any sort of BA will do. Often further education is needed to pursue a career, say in law.
A political science degree can lead to several possible careers. In law enforcement it can lead to high level positions within local or state police, the F.B.I, N.S.A or C.I.A.; outside of law enforcement a political science degree can be a stepping stone towards career in politics on the local or federal level.
There are numerous careers for a political scientist. These include activist, attorney, CIA analyst or agent, journalist, lobbyist, foreign service officer, even a freelance writer or foundation president.
Journalism is a possible career path for someone who has studied political science. News media organizations, including TV, newspapers and magazines, look for people to interpret and write about politics.