U.S. citizens do not require a Official Visa to enter Scotland. However, a U.S. passport is required:
Your U.S. passport must be valid for a minimum of 6 months from the date you plan to depart Scotland.
Your passport must have adequate unused visa pages to allow for entry and exit stamps upon arrival and departure from Scotland. Please note that Amendment pages in the back of your passport are not to be used for entry and exit stamps or visa issuance.