Vision Transformers (ViTs) have achieved state-of-the-art performance on various computer vision applications. These models, however, have considerable storage and computational overheads, making their deployment and efficient inference on edge devices challenging. Quantization is a promising approach to reducing model complexity; unfortunately, existing efforts to quantize ViTs are simulated quantization (aka fake quantization), which remains floating-point arithmetic during inference and thus contributes little to model acceleration. In this paper, we propose I-ViT, an integeronly quantization scheme for ViTs, to enable ViTs to perform the entire computational graph of inference with integer operations and bit-shifting and no floating-point operations. In I-ViT, linear operations (๐.๐., MatMul and Dense) follow the integer-only pipeline with dyadic arithmetic, and non-linear operations (๐.๐., Softmax, GELU, and LayerNorm) are approximated by the proposed lightweight integer-only arithmetic methods. In particular, I-ViT applies the proposed Shiftmax and ShiftGELU, which are designed to use integer bit-shifting to approximate the corresponding floating-point operations. We evaluate I-ViT on various benchmark models and the results show that integer-only INT8 quantization achieves comparable (or even higher) accuracy to the full-precision (FP) baseline. Furthermore, we utilize TVM for practical hardware deployment on the GPU's integer arithmetic units, achieving 3.72~4.11ร inference speedup compared to the FP model.