We measure the proper motion of the pulsar PSR J1745-2900 relative to the Galactic Center massive black hole , Sgr A* , using the Very Long Baseline Array ( VLBA ) . The pulsar has a transverse velocity of 236 \pm 11 { km s } ^ { -1 } at position angle 22 \pm 2 deg East of North at a projected separation of 0.097 pc from Sgr A* . Given the unknown radial velocity , this transverse velocity measurement does not conclusively prove that the pulsar is bound to Sgr A* ; however , the probability of chance alignment is very small . We do show that the velocity and position is consistent with a bound orbit originating in the clockwise disk of massive stars orbiting Sgr A* and a natal velocity kick of \stackrel { \scriptstyle < } { \scriptstyle \sim } 500 { km s } ^ { -1 } . An origin among the isotropic stellar cluster is possible but less probable . If the pulsar remains radio-bright , multi-year astrometry of PSR J1745-2900 can detect its acceleration and determine the full three-dimensional orbit . We also demonstrate that PSR J1745-2900 exhibits the same angular broadening as Sgr A* over a wavelength range of 3.6 cm to 0.7 cm , further confirming that the two sources share the same interstellar scattering properties . Finally , we place the first limits on the presence of a wavelength-dependent shift in the position of Sgr A* , i.e. , the core shift , one of the expected properties of optically-thick jet emission . Our results for PSR J1745-2900 support the hypothesis that Galactic Center pulsars will originate from the stellar disk and deepens the mystery regarding the small number of detected Galactic Center pulsars .