Cluster randomization trials randomize groups (called clusters) of subjects (called subunits) between intervention arms, and observations are collected from each subject. In this case, the observations among subunits of each cluster tend to be correlated. Oftentimes, the outcome of a cluster randomization trial is a time-to-event endpoint with censoring. A few sample size formulas have been proposed for time-to-event endpoint under cluster randomization. However, these formulas generally do not account for the variance of cluster sizes. We propose a new closed form sample size formula for rank tests to compare the marginal survival distributions under cluster randomization with possibly variable cluster sizes. Extensive simulation studies validates the performance of our sample size formula under various design settings.