Quantum random number generation (QRNG) harnesses the intrinsic randomness of quantum mechanical phenomena. On-chip photonic circuitry provides a robust and versatile platform that can address and explore fundamental questions in quantum as well as classical physics. Likewise, integrated waveguide-based architectures hold the potential for intrinsically scalable, efficient and compact implementations of photonic QRNG. Here, we harness the quantum emission from the two-dimensional material hexagonal boron nitride an emerging atomically thin medium that can generate single photons on demand while operating at room temperature. By means of a customized splitter arrangement, we achieve true random number generation through the measurement of single photons exiting one of four designated output ports, and subsequently verify the randomness of the sequences in accordance with the National Institute of Standards and Technology benchmark suite. Our results clearly demonstrate the viability and efficiency of this approach to on-chip deterministic random number generators.