Single-photon emitters, the basic building blocks of quantum communication and information, have been developed using atomically thin transition metal dichalcogenides (TMDCs). Although the bandgap of TMDCs was spatially engineered in artificially created defects for single-photon emitters, it remains a challenge to precisely align the emitter's dipole moment to optical cavities for the Purcell enhancement. Here, we demonstrate position- and polarization-controlled single-photon emitters in monolayer WSe. A tensile strain of ∼0.2% was applied to monolayer WSe by placing it onto a dielectric rod structure with a nanosized gap. Excitons were localized in the nanogap sites, resulting in the generation of linearly polarized single-photon emission with a g of ∼0.1 at 4 K. Additionally, we measured the abrupt change in polarization of single photons with respect to the nanogap size. Our robust spatial and polarization control of emission provides an efficient way to demonstrate deterministic and scalable single-photon sources by integrating with nanocavities.