We present a design of a majority neuron circuit with non-volatile synaptic weights. It is based on an analog majority circuit composed of controlled current inverters (CCIs). The proposed circuit is immune to device parameter fluctuations, and its fan-in is estimated about 1000. Synaptic weights are realized on the neuron circuit by adding variable resistors. We consider a design of a non-volatile synaptic weight by using a three-terminal magnetic domain-wall motion (DWM) device. The operation of a fully connected recurrent neural network composed of the proposed circuits has been confirmed by SPICE simulation.