Synthetic antiferromagnet (SAF) with high thermal stability, ultra‐fast spin dynamics, and highly efficient spin‐orbit torque switching has great application potential in neuromorphic computing hardware. However, two challenges, the weakening of Hall signal in the remanent state and the need for a large auxiliary magnetic field for perpendicular magnetization switching, greatly limit the advantages of SAF in neuromorphic computing. In this work, both the enhanced anomalous Hall resistance and magnetic‐field‐free perpendicular magnetization switching are achieved by using oblique sputtering to fabricate the Pt/CoPt/Ru/CoTb SAF with strong interlayer exchange coupling and magnetic moment compensation. The fabricated SAF as synapse shows nearly linear, nonvolatile multistate plasticity, and as neuron exhibits a nonlinear sigmoid activation function, which are used to construct a fully connected neural network with a remarkable 97.0–98.1% recognition rate for the handwritten digits. Additionally, SAF serving as spike‐timing‐dependent plasticity synapse is used to construct an adaptive, unsupervised learning spiking neural network, and achieve an 87.0% accuracy in handwritten digit recognition. The findings exhibit the promise of SAFs as specialized hardware for high‐performance neuromorphic computing, offering high recognition rates and low power consumption.