Transformer neural networks are rapidly being integrated into state-of-the-art solutions for natural language processing (NLP) and computer vision. However, the complex structure of these models creates challenges for accelerating their execution on conventional electronic platforms. We propose the first silicon photonic hardware neural network accelerator called TRON for transformer-based models such as BERT, and Vision Transformers. Our analysis demonstrates that TRON exhibits at least 14x better throughput and 8x better energy efficiency, in comparison to state-of-the-art transformer accelerators.