Devices based on spectroscopy of atomic vapors can measure physical quantities such as magnetic fields, RF electric fields, time and length, and rotation and have applications in a broad range of fields including communications, medicine, and navigation. We present a type of photonic device that interfaces single-mode silicon nitride optical waveguides with warm atomic vapors, enabling precision spectroscopy in an extremely compact (<1 cm3) package. We perform precision spectroscopy of rubidium confined in a micro-machined, 27 mm3 volume, vapor cell using a collimated free-space 120 μm diameter laser beam derived directly from a single-mode silicon nitride waveguide. With this optical-fiber integrated photonic spectrometer, we demonstrate an optical frequency reference at 780 nm with a stability of 10−11 from 1 to 104 s. This device harnesses the benefits of both photonic integration and precision spectroscopy for the next generation of quantum sensors and devices based on atomic vapors.