We propose an implementation of a CNOT gate for quantum computing based on a patterned microcavity polariton system, which can be manufactured using the modern technological facilities. The qubits are encoded in the spin-coherent polariton states. The structure consists of two wire cavities oriented at 45° with a micropillar between them. The polariton spin rotates due to the Longitudinal-Transverse splitting between polarization eigenstates in the wires. In the pillar, the optically generated circularly polarized polariton macrooccupied state plays the role of the control qubit. Because of the spin-anisotropic polariton interaction, it induces an effective magnetic field along the Z-direction with a sign depending on the qubit value.