Garry Kasparov has been an unsuccessful politician and there have been several successful politicians who have also been quite good chess players, but have any of them achieved the IM or GM title?
Some candidates who didn't quite make it -
Nathan Sharansky, who according to his Wikipedia page, was the champion of Donetsk at 15, and who beat Garry Kasparov in a simul in 1996 has never even had a rating. He was in the Israeli parliament and government in the late 90's, round about the time he beat Kasparov.
I was sure that I read somewhere that Kirsan Ilyumzhinov who, as well as being FIDE president was also president of the former Soviet republic of Kalmykia, was a master level chess player. According to his Wikipedia page he was champion of Kalmykia at the age of 14. But according to his FIDE rating profile he has only ever played in one FIDE rated blitz in 2012 where he scored 2.5/7 against opponents with an average rating of 1954 for a performance rating of 1852.
British member of parliament, Angela Eagle, was according to her Wikipedia page, British girls under 18 champion in 1976 but, again, she never got a FIDE rating let alone a title.