In this paper, the rate-distortion function of an improper-complex random source is derived. In particular, the source output is modeled by a discrete-time or a strictly band-limited continuous-time cyclostatioinary Gaussian random process. When the cycle period is unity, this model also includes stationary Gaussian processes. In order to utilize the results on the lossy compression of a real-valued wide-sense stataionary Gaussian source, a block pre-prcocessor is proposed that  asymptotically and simultaneously performs the properization and stationarization of the improper-complex cyclostationary random process. The derived rate-distorion function clearly shows how the ordinary and complementary spectral correlation functions of the process affects the inverse water filling procedure.