Multi-rater annotations commonly occur when medical images are independently annotated by multiple experts (raters). In this paper, we tackle two challenges arisen in multi-rater annotations for medical image segmentation (called ambiguous medical image segmentation): (1) How to train a deep learning model when a group of raters produces a set of diverse but plausible annotations, and (2) how to fine-tune the model efficiently when computation resources are not available for re-training the entire model on a different dataset domain. We propose a multi-rater prompt-based approach to address these two challenges altogether. Specifically, we introduce a series of rater-aware prompts that can be plugged into the U-Net model for uncertainty estimation to handle multi-annotation cases. During the prompt-based fine-tuning process, only 0.3% of learnable parameters are required to be updated comparing to training the entire model. Further, in order to integrate expert consensus and disagreement, we explore different multi-rater incorporation strategies and design a mix-training strategy for comprehensive insight learning. Extensive experiments verify the effectiveness of our new approach for ambiguous medical image segmentation on two public datasets while alleviating the heavy burden of model re-training.