CRISPR arrays are prokaryotic genomic loci consisting of repeat sequences alternating with unique spacers acquired from foreign nucleic acids. As one of the fastest-evolving parts of the genome, CRISPR arrays can be used to differentiate closely related prokaryotic lineages and track individual strains in prokaryotic communities. However, the assembly of full-length CRISPR arrays sequences remains a problem. Here, we developed SCRAMBLER, a tool that includes several pipelines for assembling CRISPR arrays from high-throughput short-read sequencing data. We assessed its performance with model data sets (Escherichia coli strains containing different CRISPR arrays and imitating prokaryotic communities of different complexities) and intestinal microbiomes of extant and extinct pachyderms. Evaluation of SCRAMBLER's performance using model data sets demonstrated its ability to assemble CRISPR arrays correctly from reads containing pairs of spacers, yielding a precision rate of >80% and a recall rate of 60-85% when checked against ground-truth data. Likewise, SCRAMBLER successfully assembled CRISPR arrays from the environmental samples, as attested by their matching with database entries. SCRAMBLER, an open-source software (github.com/biolab-tools/SCRAMBLER), can facilitate analysis of the composition and dynamics of CRISPR arrays in complex communities.