We propose an optical tensor core (OTC) architecture for neural network training. The key computational components of the OTC are the arrayed optical dot-product units (DPUs). The homodyne-detection-based DPUs can conduct the essential computational work of neural network training, i.e., matrix-matrix multiplication. Dual-layer waveguide topology is adopted to feed data into these DPUs with ultra-low insertion loss and cross talk. Therefore, the OTC architecture allows a large-scale dot-product array and can be integrated into a photonic chip. The feasibility of the OTC and its effectiveness on neural network training are verified with numerical simulations.