Many machine learning models for online applications, such as recommender systems, are often trained on data with cyclical properties. These data sequentially arrive from a time-varying distribution that is periodic in time. Existing algorithms either use streaming learning to track a time-varying set of optimal model parameters, yielding a dynamic regret that scales linearly in time; or partition the data of each cycle into multiple segments and train a separate model for each---a pluralistic approach that is computationally and storage-wise expensive.In this paper, we have designed a novel approach to overcome the aforementioned shortcomings. Our method, named "Fourier learning", encodes the periodicity into the model representation using a partial Fourier sequence, and trains the coefficient functions modeled by neural networks. Particularly, we design a Fourier multi-layer perceptron (F-MLP) that can be trained on streaming data with stochastic gradient descent (streaming-SGD), and we derive its convergence guarantees. We demonstrate Fourier learning's better performance with extensive experiments on synthetic and public datasets, as well as on a large-scale recommender system that is updated in real-time, and trained with tens of millions of samples per day.