S.C. Const. art. XVI, § 3
Whenever two-thirds of the members elected to each branch of the General Assembly shall think it necessary to call a Convention to revise, amend or change this Constitution, they shall recommend to the electors to vote for or against a Convention at the next election for Representatives; and if a majority of all the electors voting at said election shall have voted for a Convention, the General Assembly shall, at its next session, provide by law for calling the same; and such Convention shall consist of a number of members equal to that of the most numerous branch of the General Assembly.
For similar provisions in Constitution of 1868, see Const 1868, Art XV, Section 3.