The application of spin–orbit torque (SOT) devices to neuromorphic computing platforms is focused on the development of hardware circuit architectures. However, the inter-device variability, the integration modes of devices and peripheral circuits, and appropriate application scenarios are still unclear, limiting the development of SOT devices in neuromorphic computing. To solve this problem, this paper first proposes a circuit compensation scheme for the difference in resistance values of SOT devices, which solves this variability problem at the circuit level. Moreover, a synergistic scheme with the circuit is developed based on the correspondence between the multistate resistance characteristics of the SOT devices and a convolutional algorithm. To achieve this, a multichannel SOT convolutional kernel circuit architecture is built, which implements an image edge recognition application. Finally, based on a simulation model, an image edge recognition hardware circuit based on our CoPt-SOT devices is implemented, which is capable of performing image edge recognition with an accuracy of 96.33%. This scheme provides technical support and development prospects for SOT devices in neural network hardware applications.