In this Letter, the maximum likelihood (ML) estimator for the parameters of a real sinusoid in additive white Gaussian noise using irregularly-spaced samples is derived. The ML frequency estimate is first determined by a one-dimensional search, from which optimum amplitude and phase estimates are then computed. It is shown that the estimation performance of the ML method can attain Cramér-Rao lower bound when the signal-to-noise ratio is sufficiently large.