We present Agentic Aerial Cinematography: From Dialogue Cues to Cinematic Trajectories (ACDC), an autonomous drone cinematography system driven by natural language communication between human directors and drones. The main limitation of previous drone cinematography workflows is that they require manual selection of waypoints and view angles based on predefined human intent, which is labor-intensive and yields inconsistent performance. In this paper, we propose employing large language models (LLMs) and vision foundation models (VFMs) to convert free-form natural language prompts directly into executable indoor UAV video tours. Specifically, our method comprises a vision-language retrieval pipeline for initial waypoint selection, a preference-based Bayesian optimization framework that refines poses using aesthetic feedback, and a motion planner that generates safe quadrotor trajectories. We validate ACDC through both simulation and hardware-in-the-loop experiments, demonstrating that it robustly produces professional-quality footage across diverse indoor scenes without requiring expertise in robotics or cinematography. These results highlight the potential of embodied AI agents to close the loop from open-vocabulary dialogue to real-world autonomous aerial cinematography.