We present a self-consistent field theory (SCFT) formalism of topologically unconstrained ring polymers for the first time. The resulting static properties of homogeneous and inhomogeneous ring polymers are compared with the random phase approximation (RPA) results. For ring homopolymer mixture, as chi N increases, the interfacial width and segment profile converge to those of the linear polymer mixture. The critical point for the ring homopolymer system is exactly the same as the linear polymer case, (chi N)(c) = 2, since the critical point does not depend on the local structure of polymers. The critical point for ring diblock copolymer melts is (chi N)(c) = 17.795, which is similar to 1.7 times that of linear diblock copolymer melts, (chi N)(c) = 10.495. The difference results from the ring structure constraint.