Could a Jedi involve themselves in Galactic/local Politics if they hopes to?

Could an active Jedi Knight or Master be permitted to engage in Politics. Say a Jedi from Alderaan with a particular affinity for politics wanted to become a Senator, or hold a position in the Alderaanian government, could they?

Obviously we all know the inherent dangers that stem from people with power gaining political influence, but for the sake of the argument...