Text-to-music models allow users to generate nearly realistic musical audio with textual commands. However, editing music audios remains challenging due to the conflicting desiderata of performing fine-grained alterations on the audio while maintaining a simple user interface. To address this challenge, we propose Audio Prompt Adapter (or AP-Adapter), a lightweight addition to pretrained text-to-music models. We utilize AudioMAE to extract features from the input audio, and construct attention-based adapters to feedthese features into the internal layers of AudioLDM2, a diffusion-based text-to-music model. With 22M trainable parameters, AP-Adapter empowers users to harness both global (e.g., genre and timbre) and local (e.g., melody) aspects of music, using the original audio and a short text as inputs. Through objective and subjective studies, we evaluate AP-Adapter on three tasks: timbre transfer, genre transfer, and accompaniment generation. Additionally, we demonstrate its effectiveness on out-of-domain audios containing unseen instruments during training.