Clustered survival data often arise in biomedical research. When the outcome depends on the size of the cluster, the cluster size is said to be informative. Many studies assume a noninformative cluster size, even though it may not always be true. We propose a test for the assumption of informative cluster size in clustered survival data with right censoring. We use standard martingale results to obtain the asymptotic distribution of the test statistic. Simulation studies show that the proposed test works well under various scenarios. To illustrate the proposed approach, we consider several applications: periodontal data, a multicentric study of patients with liver disease, and a recent data set of patients with metastatic cancer treated using immunotherapy.