Frequency estimation of a complex single-tone in additive white Gaussian noise from irregularly-spaced samples is addressed. In this Letter, we study the periodogram and weighted phase averager, which are standard solutions in the uniform sampling scenarios, for tackling the problem. It is shown that the estimation performance of both approaches can attain the optimum benchmark of the Cramér-Rao lower bound, although the former technique has a smaller threshold signal-to-noise ratio.