A 3-regular graph \(G\) is called a 3-circulant if its adjacency matrix \(A(G)\) is a circulant matrix. We show how all disconnected 3-circulants are made up of connected 3-circulants and classify all connected 3-circulants as one of two basic types. The rank of \(A(G)\) is then completely determined for all 3-circulant graphs \(G\).