One of the most vital observational clues for unraveling the origin of Brightest Cluster Galaxies (BCG) is the observed alignment of the BCGs with their host cluster and its surroundings. We have examined the BCG-cluster alignment effect, using clusters of galaxies detected from the Sloan Digital Sky Survey (SDSS). We find that the BCGs are preferentially aligned with the principal axis of their hosts, to a much higher redshift (z >~ 0.3) than probed by previous studies (z <~ 0.1). The alignment effect strongly depends on the magnitude difference of the BCG and the second and third brightest cluster members: we find a strong alignment effect for the dominant BCGs, while less dominant BCGs do not show any departure from random alignment with respect to the cluster. We therefore claim that the alignment process originates from the same process that makes the BCG grow dominant, be it direct mergers in the early stage of cluster formation, or a later process that resembles the galactic cannibalism scenario. We do not find strong evidence for (or against) redshift evolution between 0<z<0.45, largely due to the insufficient sample size (< 200 clusters). However, we have developed a framework by which we can examine many more clusters in an automated fashion for the upcoming SDSS cluster catalogs, which will provide us with better statistics for systematic investigations of the alignment with redshift, richness and morphology of both the cluster and the BCG.