Agricultural robotics faces critical challenges in achieving energy-efficient, real-time intelligent operation under resource-constrained field conditions, where conventional computing paradigms struggle with power consumption, latency, and adaptability to dynamic environments. Neuromorphic computing, inspired by the brain's spike-based information processing and massively parallel architecture, offers transformative potential for autonomous agricultural systems by enabling ultra-low-power perception, adaptive learning, and responsive control. This review examines the integration of neuromorphic technologies—including spiking neural networks, event-based sensors, and specialized hardware platforms—into agri-robotic applications. We systematically analyze neuromorphic architectures for real-time crop monitoring, precision weed management, autonomous navigation, and robotic harvesting, highlighting their advantages in energy efficiency, temporal precision, and edge intelligence. Key neuromorphic platforms such as Intel Loihi, IBM TrueNorth, and SpiNNaker are evaluated for agricultural deployment, alongside event-driven algorithms for visual perception, sensor fusion, and motor control. Despite promising demonstrations, challenges remain in hardware-software co-design, scalability, programmability, and commercialization. This article provides a comprehensive perspective on how neuromorphic computing can revolutionize sustainable agriculture through intelligent, energy-aware robotic systems, and identifies critical research directions for translating brain-inspired computation from laboratory prototypes to practical field implementations in precision farming ecosystems.