Using 26 plates taken over the course of more than half a century, we present proper motions and photometry for 1177 stars in the central region of the Sculptor dwarf spheroidal galaxy, down to a limiting magnitude of V~20.25 at the level of the horizontal branch. The proper-motion cleaned color-magnitude diagram retained a broad giant branch, further supporting an intrinsic spread in metallicity. We determined an absolute proper motion for Sculptor, relative to background galaxies, of mu_alpha=+0.036+/-0.022arcsec/century and mu_delta=0.043+/-0.025arcsec/century after correcting for the LSR and peculiar solar motions. Our proper-motion uncertainty is similar to or smaller than those obtained by different groups for other distant satellites of the Galaxy. When combined with Sculptor's distance and radial velocity, this measurement shows the dwarf spheroidal to have a space velocity of roughly 220+/-125km/s. Although our measurement is less than twice its uncertainty, the direction of Sculptor's motion is significant because it rules out motion along the Magellanic Stream. A 2.5 sigma error allows for motion in a direction toward the Fornax dwarf spheroidal galaxy, so Sculptor remains a possible member of the proposed Fornax-Leo-Sculptor stream.