Can police make you pay a traffic violation when you get pulled over?

No, they can't. In a few states, the law allows them to accept payment when they issue a ticket. I think this is incredibly wrong and set up for fraud and police abuse. I have been stopped and was given the option of paying the police officer in South Carolina. I refused and said I would speak to the Judge. I later found out that the Police Officers took turns being the Judge for Traffic Court. Even in this situation, they allowed me to pay the fine without having the ticket go onto my record. And they kept their Word as I have the ability to check my record as the owner of an agency.