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A full Poincaré (FP) beam possesses all possible optical spin states in its cross section, which constitutes an optical analog of a skyrmion. Until now FP beams have been exclusively generated using bulk optics. Here we propose a generation scheme of an FP beam based on an optical microring cavity. We position two different angular gratings along with chiral lines on a microring cavity and generate an FP beam as a superposition of two light beams with controlled spin and orbital angular momenta. We numerically show that FP beams with tailored skyrmion numbers can be generated from this device, opening a route for developing compact light sources with unique optical spin fields.