The recently developed J-region asymptotic giant branch (JAGB) method has extraordinary potential as an extragalactic standard candle, capable of calibrating the absolute magnitudes of locally accessible Type Ia supernovae, thereby leading to an independent determination of the Hubble constant. Using Gaia Early Data Release 3 (EDR3) parallaxes, we calibrate the zero-point of the JAGB method, based on the mean luminosity of a color-selected subset of carbon-rich AGB stars. We identify Galactic carbon stars from the literature and use their near-infrared photometry and Gaia EDR3 parallaxes to measure their absolute J-band magnitudes. Based on these Milky Way parallaxes we determine the zero-point of the JAGB method to be M_J_=-6.14+/-0.05(stat)+/-0.11(sys)mag. This Galactic calibration serves as a consistency check on the JAGB zero-point, agreeing well with previously published, independent JAGB calibrations based on geometric, detached eclipsing binary distances to the LMC and SMC. However, the JAGB stars used in this study suffer from the high parallax uncertainties that afflict the bright and red stars in EDR3, so we are not able to attain the higher precision of previous calibrations, and ultimately will rely on future improved DR4 and DR5 releases.