Geoffrey C. Bower, Adam T. Deller, Paul B. Demorest, Jason Dexter, Andreas Brunthaler, Gregory Desvignes, Ralph P. Eatough, Heino Falcke, Ciriaco Goddi, Michael Kramer, F. Yusef-Zadeh

We present new astrometric observations of the Galactic Center magnetar, PSR J1745-2900, with the Very Long Baseline Array (VLBA). Combined with previously published measurements in 10 epochs that spanned 477 days, the complete data set consists of 25 epochs and 41 independent measurements that span 1984 days. These data constrain the proper motion to an accuracy of $\lesssim 2\%$ and set an upper limit on the absolute value of the magnetar's acceleration of $\lesssim (0.4, 0.2)\, {\rm mas\,y^{-2}}$ in the two celestial coordinates, consistent with the maximum value of $\sim 0.03\,{\rm mas\,y^{-2}}$ expected for an orbit around Sgr A*. Future measurements have the potential to detect the acceleration of PSR J1745-2900 due to Sgr A* should PSR J1745-2900 re-brighten. We consider several potential sources of systematic variations in the astrometric residuals after fitting for standard parameters, including refractive wander, changes in the structure of Sgr A*, and the presence of an unseen binary companion. While a stellar companion model can be fit to the astrometric data, pulse period measurements are inconsistent with that model. No changes in the apparent image size of the magnetar were detected over the duration of these observations, indicating a lack of change in the properties of the line-of-sight scattering during this period. We also show that the upper limit to the mean core shift of Sgr A* is consistent with expectations for a compact jet or symmetric accretion flow.