A scheme is presented to realize nonreciprocal photon blockade by exploiting a spinning optomechanical resonator, where the photon blockade effect appears when the spinning resonator is driven from one side but vanishes from the other side. This quantum nonreciprocity originates from the Sagnac effect and Kerr-type interaction between photons in the spinning resonator. We analyze the dynamics of the system in the weak driving regime, and discuss the photon statistical properties by calculating the second-order correlation function. Based on master-equation simulations, we also study numerical results of the steady state of the system and the validity of the analytical solution, and find that it is feasible to achieve nonreciprocal photon blockade by choosing appropriate parameters in a spinning optomechanical resonator.