AskHistorians

AFAIK the two parties became associated with their specific colors in the 2000 election when one of the major news outlets was doing live coverage of the election. They had a graphic of the country with each state marked red/blue depending on which party had won that state, and were referring to them as red or blue states. Apparently before that point, the parties didnt have specific colors associated, and in fact red was still heavily associated with communism.