We theoretically study an exciton-polariton Josephson junction in a planar semiconductor microcavity.When an external magnetic field is applied normal to the plane of the microcavity,remarkable competition is found between the Zeeman energy and the interactions of exciton polaritons.We can determine a critical value for the magnetic field,below which there is only the DC Josephson effect,and above which the AC Josephson effect appears.