In many cluster randomization studies, cluster sizes are not fixed and may be highly variable. For those studies, sample size estimation assuming a constant cluster size may lead to under-powered studies. Sample size formulas have been developed to incorporate the variability in cluster size for clinical trials with continuous and binary outcomes. Count outcomes frequently occur in cluster randomized studies. In this paper, we derive a closed-form sample size formula for count outcomes accounting for the variability in cluster size. We compare the performance of the proposed method with the average cluster size method through simulation. The simulation study shows that the proposed method has a better performance with empirical powers and type I errors closer to the nominal levels.