Accurate monitoring of the State of Charge (SOC) is crucial for mitigating the risks of overcharging or overdischarging and ensuring the healthy operation of lithium-ion batteries. Particle Filter (PF) has emerged as a prominent method for estimating the SOC of lithium-ion batteries due to its unique advantages in handling nonlinear and non-Gaussian systems. However, traditional resampling methods suffer from particle diversity depletion, making it difficult to comprehensively cover the posterior distribution of the true state, thereby leading to low state estimation accuracy. To address this issue, this paper introduces a quantum rotation gate into the Metropolis-Hastings (M-H) sampling-based resampling mechanism, proposing a novel quantum M-H resampling method. First, based on the principle of quantum superposition states, particle quantization, measurement collapse, and quantum rotation gate operations are employed to construct a sampling distribution using the quantum rotation gate, replacing the Gaussian mutation in the original M-H resampling mechanism. Second, an adaptive selection strategy is adopted to generate new particles using either the quantum rotation gate or crossover-based sampling distributions, with a probabilistic acceptance or rejection mechanism for the new particles. Finally, the SOC is estimated through weighted summation of the particles. The effectiveness of the proposed method is validated using a one-dimensional univariate time series model and lithium-ion battery SOC estimation. Experimental results demonstrate that, compared to existing resampling methods, the proposed approach significantly improves the quality of resampled particles and enhances the accuracy of PF in estimating the SOC of lithium-ion batteries.