The cycle frequencies of a cyclostationary signal can be used for the signal identification and classification, separation of the overlapped signals in cycle domain, and so on. Efficient cycle frequency acquisition depends on the fast measurement of cyclic autocorrelation function (CAF) or spectral correlation function (SCF) of the signal. Presently the relative efficient CAF and SCF measuring methods mainly include the cyclic correlogram, the well-known fast Fourier transform accumulation method (FAM), and so on. Motivated by these methods, a new efficient cycle frequency acquisition method which integrates the fast Fourier transform (FFT) algorithm with the autocorrelated cyclic autocorrelation function, named FACA, is presented. With the presented method, we can acquire the cycle frequencies of a cyclostationary signal more efficiently with a given level of reliability. Meanwhile, by enlarging the FFT window width of the FACA method we can get the same cycle frequency resolution as the benchmarked method FAM, but the computation cost still can be spared at this case.