A diamond nano-crystal hosting a single nitrogen vacancy (NV) center is optically selected with a confocal scanning microscope and positioned deterministically onto the subwavelength-diameter waist of a tapered optical fiber (TOF) with the help of an atomic force microscope. Based on this nano-manipulation technique we experimentally demonstrate the evanescent coupling of single fluorescence photons emitted by a single NV-center to the guided mode of the TOF. By comparing photon count rates of the fiber-guided and the free-space modes and with the help of numerical FDTD simulations we determine a lower and upper bound for the coupling efficiency of (9.5+/-0.6)% and (10.4+/-0.7)%, respectively. Our results are a promising starting point for future integration of single photon sources into photonic quantum networks and applications in quantum information science.