Accurate document retrieval is crucial for the success of retrieval-augmented generation (RAG) applications, including open-domain question answering and code completion. While large language models (LLMs) have been employed as dense encoders or listwise rerankers in RAG systems, they often struggle with reasoning-intensive tasks because they lack nuanced analysis when judging document relevance. To address this limitation, we introduce JudgeRank, a novel agentic reranker that emulates human cognitive processes when assessing document relevance. Our approach consists of three key steps: (1) query analysis to identify the core problem, (2) document analysis to extract a query-aware summary, and (3) relevance judgment to provide a concise assessment of document relevance. We evaluate JudgeRank on the reasoning-intensive BRIGHT benchmark, demonstrating substantial performance improvements over first-stage retrieval methods and outperforming other popular reranking approaches. In addition, JudgeRank performs on par with fine-tuned state-of-the-art rerankers on the popular BEIR benchmark, validating its zero-shot generalization capability. Through comprehensive ablation studies, we demonstrate that JudgeRank's performance generalizes well across LLMs of various sizes while ensembling them yields even more accurate reranking than individual models.