Referring Expression Comprehension (REC), which aims to ground a local visual region via natural language, is a task that heavily relies on multimodal alignment. Most existing methods utilize powerful pre-trained models to transfer visual/linguistic knowledge by full fine-tuning. However, full fine-tuning the entire backbone not only breaks the rich prior knowledge embedded in the pre-training, but also incurs significant computational costs. Motivated by the recent emergence of Parameter-Efficient Transfer Learning (PETL) methods, we aim to solve the REC task in an effective and efficient manner. Directly applying these PETL methods to the REC task is inappropriate, as they lack the specific-domain abilities for precise local visual perception and visual-language alignment. Therefore, we propose a novel framework of Multimodal Prior-guided Parameter Efficient Tuning, namely MaPPER. Specifically, MaPPER comprises Dynamic Prior Adapters guided by an aligned prior, and Local Convolution Adapters to extract precise local semantics for better visual perception. Moreover, the Prior-Guided Text module is proposed to further utilize the prior for facilitating the cross-modal alignment. Experimental results on three widely-used benchmarks demonstrate that MaPPER achieves the best accuracy compared to the full fine-tuning and other PETL methods with only 1.41% tunable backbone parameters. Our code is available at https://github.com/liuting20/MaPPER.