This paper addresses the problem of issue-commit link recovery for improving software traceability. Existing AI/ML-based approaches suffer from limited context windows and inefficiencies in analyzing individual issue-commit pairs. To overcome these limitations, we present LinkAnchor, an autonomous agent based on a large-scale language model (LLM). LinkAnchor efficiently leverages rich context, including commit history, issue comments, and code files, through a lazy-access architecture. Instead of manually evaluating all candidate commits, it automatically identifies the target commit. Experimental results demonstrate that LinkAnchor outperforms existing state-of-the-art methods by 60-262% in Hit@1 scores. It is released as an open-source, scalable tool compatible with GitHub and Jira.