If a person opens a business credit card for his/her business, will that business credit card affect his/her personal credit score in any way?

If so, will it be in a positive or negative way?

If the business card is opened under your name and SSN, then yes it can affect your personal credit score, just as a card would with just your name and SSN only. As long as you keep your business account in good standing just as you would your other accounts (no late/past due payments, no overlimits, etc) then you'll be ok.