This paper proposes a new state of charge estimation method inspired by the Fourier neural operator. The Fourier neural operator is capable of learning entire nonlinear dynamics of any partial differential equations. The complicated nonlinear dynamics of battery parameters is well captured by a flexible, efficient and expressive structure of the Fourier neural operators. Extensive numerical experiments and tests with a publicly available data as well as with our own data are conducted to demonstrate the noise-tolerance, time window independence, temperature generalization and transfer learning features of the proposed method. Our proposed method, as a robust SOC estimator, performs better than the other methods considered previously and the performances are in competitive manner with any state-of-the-art machine learning based methods.