The absolute mass of a cluster can be measured by the gravitational lens magnification of a background galaxy population. We have made the first application of this method to measure mass in the cluster Abell 1689, taking into account the uncertainties introduced by intrinsic clustering of the background galaxies, shot-noise, and the effects of strong magnification near the cluster center. We present mass maps and the mass profile. In a cylinder of radius 0.24 h-1Mpc (2'.2) around the peak, we find the projected mass is M2 d(< 0.24 h-1Mpc) = (0.50±0.09) × 10 15h-1M☉. Our results are in good agreement with those from the shear analysis.