The image geolocalization task aims to predict the location where an image was taken anywhere on Earth using visual clues. Existing large vision-language model (LVLM) approaches leverage world knowledge, chain-of-thought reasoning, and agentic capabilities, but overlook a common strategy used by humans -- using maps. In this work, we first equip the model \textit{Thinking with Map} ability and formulate it as an agent-in-the-map loop. We develop a two-stage optimization scheme for it, including agentic reinforcement learning (RL) followed by parallel test-time scaling (TTS). The RL strengthens the agentic capability of model to improve sampling efficiency, and the parallel TTS enables the model to explore multiple candidate paths before making the final prediction, which is crucial for geolocalization. To evaluate our method on up-to-date and in-the-wild images, we further present MAPBench, a comprehensive geolocalization training and evaluation benchmark composed entirely of real-world images. Experimental results show that our method outperforms existing open- and closed-source models on most metrics, specifically improving Acc@500m from 8.0\% to 22.1\% compared to \textit{Gemini-3-Pro} with Google Search/Map grounded mode.