In the domain of computer vision, transformer models have shown noteworthy success, prompting extensive research on optimizing their inference, particularly concerning their deployment on edge devices. While quantization has emerged as a viable solution for enabling energy efficiency in Convolutional Neural Networks (CNNs), achieving direct quantization of complex activation and normalization operators in transformer models proves to be a challenging task. Existing methods that rely on 64-bit integers often suffer from data truncation issues when deployed to energy-constrained edge devices, resulting in a significant loss of model accuracy. In this paper, we propose a range-constrained quantization technique for activation and normalization operators in transformers that addresses the dilemma between data range and precision. Our approach is the first 32-bit integer-based edge kernel implementation for vision transformers with post-training integer-only quantization, ensuring both efficiency and accuracy. Experimental results demonstrate a remarkable 5 times kernel speedup when deployed on two different ARM CPUs, with negligible accuracy loss in comparison to full-precision vision transformers. This innovative work is poised to significantly impact the deployment of transformer models on energy-efficient edge devices.