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Agriculture is increasingly challenged by climate variability, resource scarcity, and the need for more efficient and sustainable farm management. Although artificial intelligence has shown strong potential in tasks such as crop monitoring, disease diagnosis, irrigation support, and field robotics, most current systems remain task-specific and operate as isolated analytical or decision-support modules. This paper presents a prospective view of agentic AI in agriculture as an emerging systems paradigm for automatic farming. We distinguish AI-assisted agriculture from agentic agricultural systems, organize recent literature into four directions, and propose a framework for automatic farming systems centered on multimodal perception, specialized decision components, orchestration, bounded actuation, and continuous feedback under human oversight. We also discuss the main challenges for real-world deployment, including partial observability, heterogeneity, multi-objective decision-making, safety, and evaluation. The paper argues that the next step for agricultural AI is not only improved task-level performance, but the design of coherent farm-scale systems able to perceive, reason, and act under real operational constraints.