Cryo-electron microscopy recently experienced great improvements in structure resolution due to direct electron detectors with improved contrast and fast read-out leading to single electron counting. High frames rates enabled dose fractionation, where a long exposure is broken into a movie, permitting specimen drift to be registered and corrected. The typical approach for image registration, with high shot noise and low contrast, is multi-reference (MR) cross-correlation. Here we present the software package Zorro, which provides robust drift correction for dose fractionation by use of an intensity-normalized cross-correlation and logistic noise model to weight each cross-correlation in the MR model and filter each cross-correlation optimally. Frames are reliably registered by Zorro with low dose and defocus. Methods to evaluate performance are presented, by use of independently-evaluated even- and odd-frame stacks by trajectory comparison and Fourier ring correlation. Alignment of tiled sub-frames is also introduced, and demonstrated on an example dataset. Zorro source code is available at github.com/CINA/zorro.