There is absolutely no barrier to a ger becoming a Rov. there are many examples in the time of the gemoro that gerim were very prominent Tanaim (mibnei bonim shel homon horosho lomdu torah bivnei brak, shmaya ,avtalion, Unkelos hager, rabbi akiva desended from gerim)
There is a prohibition on making him KING (not just any communal position) ‘mikerev achechu tossim olechu melech”. Devorim 17-15. from amongst your “brothers” you should make a king. A ger is not considered “from amongst your brothers”.