Low-bit quantization is essential for efficient LLM inference, and both rotation and fine-grained group quantization have shown individual promise. However, their combination often leads to accuracy degradation or hardware overhead due to a mismatch between the global nature of rotation and the localized behavior of group scaling. We propose GyRot, a quantization framework and hardware accelerator that bridges this gap through algorithm-hardware co-design. GyRot introduces Coarse Rotation, Fine Grouping (CoRFiG) and Harmonic-Aligned Permutation (HAP) to enable cooperative integration of rotation and group quantization, enhancing quantizability while relaxing scaling factor precision. To further reduce hardware cost, we reformulate asymmetric quantization and introduce a zero-point rounding strategy that enables fully integer dequantization. Implemented on an INT4-based tensor PE architecture, GyRot achieves state-of-the-art 4-bit accuracy across LLaMA-family models, while delivering up to 3.4× speedup and 3.6× energy efficiency over baseline LLM accelerators. These results validate GyRot's practical effectiveness for scalable and energy-efficient LLM deployment.