Yes a felon can be a politician.
There's no law that says that a convicted felon cannot run for office and be a politician or even run for president.
There have been a few convicted felons that have changed there ways and have become politicians and turned out to be good politicians.
There's also been some convicted felons that have changed their lives around for the better and have become mayors of towns.
Those convicted felons really did change and became great members of society and became great mayors and politicians.
Just because someone has been in prison for something bad doesn't mean they cannot change and be a good person and be a good person in office.