Aspect Sentiment Quad Prediction (ASQP) has seen significant advancements, largely driven by the powerful semantic understanding and generative capabilities of large language models (LLMs). However, while syntactic structure information has been proven effective in previous extractive paradigms, it remains underutilized in the generative paradigm of LLMs due to their limited reasoning capabilities. In this paper, we propose S^2IT, a novel Stepwise Syntax Integration Tuning framework that progressively integrates syntactic structure knowledge into LLMs through a multi-step tuning process. The training process is divided into three steps. S^2IT decomposes the quadruple generation task into two stages: 1) Global Syntax-guided Extraction and 2) Local Syntax-guided Classification, integrating both global and local syntactic structure information. Finally, Fine-grained Structural Tuning enhances the model's understanding of syntactic structures through the prediction of element links and node classification. Experiments demonstrate that S^2IT significantly improves state-of-the-art performance across multiple datasets. Our implementation will be open-sourced at https://github.com/DMIRLAB-Group/S2IT.