This study aims to exploit the resistance states of Cr/ZnO/TiN memristors to generate random numbers. A random number generator (RNG) circuit employing a single memristor is proposed. We suggest that current compliance (CC) is a significant parameter in determining the quality of randomness; it is found that low CCs (20-50 μA) have a wide resistance state distribution that facilitates random bits. This work provides insight into the implementation of memristors for data security applications.