We have measured the absolute proper motion of the young globular cluster Pal 12 with respect to background galaxies, using plate material spanning a 40 yr time baseline, and measuring stars down to a magnitudeV ∼ 22. The measured absolute proper motion has an uncertainty of 0.3 mas yr^-1 in each coordinate. Pal 12's young age for a globular cluster led to the hypothesis that the cluster originated in the Large Magellanic Cloud (LMC) and was later captured by the Milky Way (Lin & Richer). Here we investigate this hypothesis using the complete kinematical data. We present the orbital characteristics of Pal 12 and compare them with those of the LMC and Sagittarius dwarf galaxy (Sgr). The present kinematical data suggest that, from the two parent candidates for Pal 12, Sgr presents a more plausible case for the host galaxy than the LMC. We explore this scenario in the context of the uncertainties in the orbits and using two different analyses: the direct comparison of the orbits of Pal 12 and Sgr as a function of time, and the analytical model of Sgr's tidal disruption developed by Johnston. We find that, within the present uncertainties of the observables, this scenario is viable in both methods. Moreover, both methods place this event at the same point in time. Our best estimate of the time of Pal 12's tidal capture from Sgr is ∼1.7 Gyr ago.