South Carolina doesn’t have a Franchise Tax by name, but does have an “Annual License Fee” for Corporations that closely resemble a Franchise Tax. It applies to Corporations transacting or conducting business within South Carolina. It's typically filed by a Tax Accountant because it is literally part of the state income tax filing.
Annual License Fees are due at the same time as the Annual Report, which is filed as part of the C Corporation Income Tax Return or request for extension, each year by the 15th day of the fourth month after the end of your business year.
C Corporations must pay an annual License Fee which is 0.1% of capital and paid in surplus, plus $15.