Visual grounding, the task of linking textual queries to specific regions within images, plays a pivotal role in vision-language integration. Existing methods typically rely on extensive task-specific annotations and fine-tuning, limiting their ability to generalize effectively to novel or out-of-distribution scenarios. To address these limitations, we introduce GroundingAgent, a novel agentic visual grounding framework that operates without any task-specific fine-tuning. GroundingAgent employs a structured, iterative reasoning mechanism that integrates pretrained open-vocabulary object detectors, multimodal large language models (MLLMs), and large language models (LLMs) to progressively refine candidate regions through joint semantic and spatial analyses. Remarkably, GroundingAgent achieves an average zero-shot grounding accuracy of 65.1% on widely-used benchmarks (RefCOCO, RefCOCO+, RefCOCOg), entirely without fine-tuning. Furthermore, by substituting MLLM-generated captions with the original query texts, the accuracy at the selection stage alone reaches approximately 90%, closely matching supervised performance and underscoring the critical role of LLM reasoning capabilities. GroundingAgent also offers strong interpretability, transparently illustrating each reasoning step, thus providing clear insights into its decision-making process.