<p>The spin–orbit coupling (SOC) effect is fundamental to emerging quantum technologies, underpinning phenomena from topological phases to spintronic functionalities. However, the accelerated discovery of SOC-driven materials is severely hindered by the high computational cost of relativistic density functional theory and the limited transferability of existing machine learning models. Here, to address these challenges, we introduce Uni-HamGNN, a universal graph neural network designed to predict SOC Hamiltonians across the periodic table. By using a physics-informed decomposition, we separate the Hamiltonian into spin-independent components and symmetry-preserving SOC correction terms. This formulation enables a robust delta-learning strategy that fits these components independently, effectively mitigating training instabilities caused by their disparate energy scales and allowing efficient model training on a resource-optimized dataset. Uni-HamGNN achieves high predictive accuracy and broad applicability, as demonstrated through high-throughput screening of the GNoME dataset, where it successfully identified 138 topological insulators from thousands of candidates. Furthermore, the model captures subtle relativistic effects in complex systems, yielding precise predictions of valley polarization in two-dimensional materials and of twist-angle-dependent electronic structures in transition metal dichalcogenide heterostructures. By eliminating the need for system-specific retraining and bypassing costly SOC-density functional theory calculations, Uni-HamGNN provides a robust, transferable framework that substantially accelerates the data-driven discovery and design of next-generation quantum materials.</p>