Inspired by the recent success of an artificial neural network (ANN) based system, known as charge-domain computing (CDC), we propose a novel framework for spiking neural networks (SNNs) called RC-Spike. In RC-Spike, synaptic currents are accumulated with resistively coupled synapses, with which circuit implementation can be simplified compared with CDC circuits. Because of this resistive coupling effect, a neuron in RC-Spike does not compute an exact dot product. However, RC-Spike can be successfully trained in the framework of SNNs, and we show that the learning performance of RC-Spike is as high as ANNs on the MNIST and Fashion-MNIST datasets.