Domain adaptive object detection (DAOD) aims to generalize detectors trained on an annotated source domain to an unlabelled target domain.As the visual-language models (VLMs) can provide essential general knowledge on unseen images, freezing the visual encoder and inserting a domain-agnostic adapter can learn domain-invariant knowledge for DAOD.However, the domain-agnostic adapter is inevitably biased to the source domain.It discards some beneficial knowledge discriminative on the unlabelled domain, \ie domain-specific knowledge of the target domain.To solve the issue, we propose a novel Domain-Aware Adapter (DA-Ada) tailored for the DAOD task.The key point is exploiting domain-specific knowledge between the essential general knowledge and domain-invariant knowledge.DA-Ada consists of the Domain-Invariant Adapter (DIA) for learning domain-invariant knowledge and the Domain-Specific Adapter (DSA) for injecting the domain-specific knowledge from the information discarded by the visual encoder.Comprehensive experiments over multiple DAOD tasks show that DA-Ada can efficiently infer a domain-aware visual encoder for boosting domain adaptive object detection.Our code is available at https://github.com/Therock90421/DA-Ada.