Memristor devices can be utilized for various computing applications, and stochastic computing is one of them. The intrinsic stochastic characteristics of the memristor cause unpredictable current fluctuations by the capture and emission of electrons in a trap site. Herein, a true random number generator (TRNG) using the random telegraph noise (RTN) of the memristor as an entropy source is proposed. TiOx/Al2O3 memristors are fabricated, and the capture time probability of the RTN characteristics is modulated to 50% with varying read‐voltage and device conductance state. In addition, the TRNG operations with the RTN current signals as entropy sources are experimentally demonstrated with a customized breadboard, and the randomness is verified with the National Institute of Standards and Technology (NIST) tests.