Anderson localization of light is a fundamental emergent phenomenon in disordered systems. In arrays of coupled waveguides, it suppresses transport and causes photons to remain localized near the excitation site as coupling disorder increases. Here, we experimentally demonstrate Anderson localization using single photons emitted by a single-photon emitter in hexagonal boron nitride at room temperature. Despite the limited temporal coherence of the emitter, the photons undergo pronounced Anderson localization, evidenced by exponentially localized output intensity profiles in laser-written disordered waveguide lattices, for excitation both in the bulk of the array and at its boundary. Beyond the experimental demonstration, we develop a general theoretical framework for wave propagation in disordered tight-binding systems, showing that the configuration-averaged output intensity converges to a stationary spatial distribution at large propagation distances and that finite temporal coherence does not by itself restore discrete diffraction under time-integrated detection. In the case of off-diagonal disorder, this stationary profile is characterized by an effective localization length $\xi$ that follows the inverse-variance law $\xi \sim 1/{\sigma }^2$, where ${\sigma }^2=Var(ln\kappa )$ is the variance of the logarithmic couplings, with a prefactor of order unity that becomes constant in the weak-disorder limit. These results establish defect-based room-temperature emitters as practical platforms for studying Anderson localization in integrated photonics and support their use in applications that exploit controlled disorder, including neuromorphic and quantum photonic architectures.