The pull request (PR)-based software development mechanism is of great significance in the practice of open-source software. Appropriate code reviewers can assist contributors in detecting potential errors in PRs through code review, thus providing quality assurance for the continuous development and integration process. However, the complexity of code change content and the inherent diversity of review behaviors enhance the difficulty of reviewer recommendation. The existing methods mainly concentrate on mining the semantic information of changed codes from PRs or constructing reviewer portraits based on review history and then making recommendations through various static strategy combinations. These studies are restricted by the richness of model training corpora and the complexity of interaction types, leading to unsatisfactory recommendation performance. Given this, this study proposes a novel code reviewer recommendation method based on inter-agent collaboration. This method utilizes advanced large language models to accurately capture the rich textual semantics information of PRs and reviewers. Moreover, the powerful planning, collaboration, and decision-making capabilities of AI agents enable the integration of information from different interaction types, possessing high flexibility and adaptability. The experimental analysis based on real datasets shows that compared with the baseline reviewer recommendation methods, the performance of the proposed method is improved by 4.45% to 26.04%. In addition, the case study proves that the proposed method has outstanding performance in interpretability, further verifying its effectiveness and reliability in practical applications.