Non-Gaussianity of noises and non-stationarity of signals have been the two crucial considerations in the fields of signal processing and communications. Correspondingly, many denoising and cyclostationary methods have been published to deal with the relevant problems, respectively. Recently, a novel method named cyclic correntropy or cyclostationary correntropy was proposed to deal with the two problems simultaneously. Thanks to the symmetry and sparsity of cyclic correntropy spectrum, the compressed spectrum obtained by compressive sensing can be used to complete the task in certain situations. In this letter, a novel method to estimate the cyclic frequency by compressed cyclic correntropy spectrum is proposed to reduce computational complexity and storage cost. To reveal the proposed method's effectiveness and robustness to impulsive noise, a number of numerical experiments are carried out to compare with existing cyclostationary methods. As cyclostationary signal processing and compressive sensing are the two great theories, through in-depth study, they can have more collaborative work opportunities and meanings.