The zero point of measured photospheric Doppler shifts is uncertain for at least two reasons: instrumental variations (from, e.g., thermal drifts), and the convective blueshift, a known correlation between intensity and upflows. Calibrated Doppler velocities would be useful for (i) improving estimates of the Poynting flux of magnetic energy across the photosphere, and (ii) constraining processes underlying flux cancellation, the mutual apparent loss of magnetic flux in closely spaced, opposite-polarity magnetogram features. We present a method to absolutely calibrate line-of-sight (LOS) velocities in solar active regions (ARs) near disk center using three successive vector magnetograms and one Dopplergram coincident with the central magnetogram. It exploits the fact that Doppler shifts measured along polarity inversion lines (PILs) of the LOS magnetic field determine one component of the velocity perpendicular to the magnetic field, and optimizes consistency between changes in LOS flux near PILs and the transport of transverse magnetic flux by LOS velocities, assuming ideal electric fields govern the magnetic evolution. We apply our method to vector magnetograms of AR 11158, observed by the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory, and find clear evidence of offsets in the Doppler zero point, in the range of 50 -- 550 m s$^{-1}$. In addition, we note that a simpler calibration can be determined from an LOS magnetogram and Dopplergram pair from the median Doppler velocity among all near-disk-center PIL pixels. We briefly discuss shortcomings in our initial implementation, and suggest ways to address these. In addition, as a step in our data reduction, we discuss use of temporal continuity in the transverse magnetic field direction to correct apparently spurious fluctuations in resolution of the 180$^circ$ ambiguity.
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