We propose an agentic zero-shot approach for finding entity mentions in natural-language text and linking them to canonical entities in a given knowledge graph. Our approach is based on large language models (LLMs) using tool calls to explore the knowledge graph (KG) and to annotate the text. We implement our approach in GRASP, a framework for agentic KG-based tasks, and evaluate it on five entity-linking benchmarks including KORE50 and AIDA-CoNLL using small and large, open-source and proprietary LLMs. Our system achieves an average F1-score over all five benchmarks of 80.3% with Kimi K2.7 Code compared to 72.6% using ReFinED, a state-of-the-art non-agentic entity linker.