Large Language Models (LLMs) have recently been explored as fine-grained zero-shot re-rankers by leveraging attention signals to estimate document relevance. However, existing methods either aggregate attention signals across all heads or rely on a statically selected subset identified by heuristic rules. This solution can be suboptimal because the informative heads can vary across queries or domains. Moreover, naively combining multiple heads can degrade performance due to redundancy or conflicting ranking signals. In this paper, we propose a query-dependent head selection method, RouteHead, for attention-based re-ranking with LLMs. Specifically, we learn a lightweight router that can map each query to an optimal head set, and relevance scores are computed by aggregating attention signals only from these heads. Since query-to-head optimal labels are unavailable, we first construct pseudo labels via an offline search. The router represents each head with a learnable embedding and represents each query using an embedding extracted from the hidden states of the frozen LLM. Then it is trained on the pseudo labels with a sparsity regularizer. Experiments on diverse benchmarks and multiple LLM backbones show that the proposed method consistently outperforms strong baselines.