Domain adaptive object detection (DAOD) aims to generalize detectors trained on an annotated source domain to an unlabelled target domain. However, existing methods focus on reducing the domain bias of the detection backbone by inferring a discriminative visual encoder, while ignoring the domain bias in the detection head. Inspired by the high generalization of vision-language models (VLMs), applying a VLM as the robust detection backbone following a domain-aware detection head is a reasonable way to learn the discriminative detector for each domain, rather than reducing the domain bias in traditional methods. To achieve the above issue, we thus propose a novel DAOD framework named Domain-Aware detection head with Prompt tuning (DA-Pro), which applies the learnable domain-adaptive prompt to generate the dynamic detection head for each domain. Formally, the domain-adaptive prompt consists of the domain-invariant tokens, domain-specific tokens, and the domain-related textual description along with the class label. Furthermore, two constraints between the source and target domains are applied to ensure that the domain-adaptive prompt can capture the domains-shared and domain-specific knowledge. A prompt ensemble strategy is also proposed to reduce the effect of prompt disturbance. Comprehensive experiments over multiple cross-domain adaptation tasks demonstrate that using the domain-adaptive prompt can produce an effectively domain-related detection head for boosting domain-adaptive object detection. Our code is available at https://github.com/Therock90421/DA-Pro.