Low-cost devices with ultra-low power radio capabilities are a major challenge in smart devices, while a permanently-on receiver is required for smart communication. This paper proposes a wake-up radio with a neuromorphic preprocessing system both biased in weak inversion region. The system is able to receive a 2.4 GHz signal, demodulate it, and recognize bit patterns based on the spiking frequency of a neuron. Significant performance is obtained with 1.2 nW of total power consumption, which is at least three orders of magnitude less than the conventional RF envelope detectors. Further, spiking frequency responsiveness over input power suggests that the proposed system can distinguish different signals at 2.4 GHz. The proposed system achieves an energy efficiency of 1.2 pJ/bit with a minimum detectable signal of-27 dBm.