Robotic kitting has attracted considerable attention in logistics and industrial settings. However, existing kitting methods encounter challenges such as low precision and poor efficiency, limiting their widespread applications. To address these issues, we present a novel kitting framework that improves both the precision and computational efficiency of complex kitting tasks. Firstly, our approach introduces a fine-grained orientation estimation technique in the picking module, significantly enhancing orientation precision while effectively decoupling computational load from orientation granularity. This approach combines an SO(2)-equivariant network with a group discretization operation to preciously predict discrete orientation distributions. Secondly, we develop the Hand-tool Kitting Dataset (HKD) to evaluate the performance of different solutions in handling orientation-sensitive kitting tasks. This dataset comprises a diverse collection of hand tools and synthetically created kits, which reflects the complexities encountered in real-world kitting scenarios. Finally, a series of experiments are conducted to evaluate the performance of the proposed method. The results demonstrate that our approach offers remarkable precision and enhanced computational efficiency in robotic kitting tasks.