Reasonably designing high-capacity novel electrode materials is key to further enhancing the energy density of ion batteries. Graphene has been considered one of the most promising candidates for anodes in ion batteries. However, the weak interaction between pure graphene and the corresponding ions results in a low theoretical capacity. Based on this, in this work the first-principles calculation is used to assess the viability of two-dimensional Cu/NO₂G, a single-atom copper-doped graphene anchored by nitrogen and oxygen, as an anode material for Li/Na/K-ion batteries. The results show that Cu/NO₂G is stable in terms of thermodynamics and kinetics. It maintains good conductivity before and after the adsorption of Li/Na/K, with theoretical capacities of 1639.9 mAh/g for lithium, 2025.8 mAh/g for sodium, and 1157.6 mAh/g for potassium. In the embedding process of Li/Na/K, the lattice constant changes minimally (less than 1%), indicating excellent cycling stability. Additionally, the migration energy barriers for Li, Na, and K on the surface of Cu/NO₂G are 0.339 eV, 0.209 eV, and 0.098 eV, respectively, demonstrating its superior rate performance. In summary, these results provide a solid theoretical foundation for rationally designing metal single-atom doped graphene as a novel anode material for alkali metal ion batteries. All the data presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00213.00063.