It does not have an adverse affect... your score may go down because part of your score is calculated by the percentage of available credit that you utilize and if you close a paid off account, your available credit goes down..which could make your percentage of available credit utilized go up, which could affect your credit score... but closing an account on its own will not affect your credit score.
best to just pay the card off, switch to paper statements and make them send you statements for the next 20-30 years... and never use the card again.