The BABAR Silicon Vertex Tracker (SVT) is a five-layer double-sided silicon detector designed to provide precise measurements of the position and direction of primary tracks, and to fully reconstruct low-momentum tracks produced in e+e- collisions at the PEP-II asymmetric collider at Stanford Linear Accelerator Center. This paper describes the design, implementation, performance, and validation of the local alignment procedure used to determine the relative positions and orientations of the 340 SVT wafers. This procedure uses a tuned mix of in-situ experimental data and complementary lab-bench measurements to control systematic distortions. Wafer positions and orientations are determined by minimizing a chisquared computed using these data for each wafer individually, iterating to account for between-wafer correlations. A correction for aplanar distortions of the silicon wafers is measured and applied. The net effect of residual mis-alignments on relevant physical variables is evaluated in special control samples. The BABAR data-sample collected between November 1999 and April 2008 is used in the study of the SVT stability.