Conventional CRISPR-Cas systems maintain genomic integrity by leveraging guide RNAs for the nuclease-dependent degradation of mobile genetic elements, including plasmids and viruses. Here we describe a notable inversion of this paradigm, in which bacterial Tn7-like transposons have co-opted nuclease-deficient CRISPR-Cas systems to catalyse RNA-guided integration of mobile genetic elements into the genome. Programmable transposition of Vibrio cholerae Tn6677 in Escherichia coli requires CRISPR- and transposon-associated molecular machineries, including a co-complex between the DNA-targeting complex Cascade and the transposition protein TniQ. Integration of donor DNA occurs in one of two possible orientations at a fixed distance downstream of target DNA sequences, and can accommodate variable length genetic payloads. Deep-sequencing experiments reveal highly specific, genome-wide DNA insertion across dozens of unique target sites. This discovery of a fully programmable, RNA-guided integrase lays the foundation for genomic manipulations that obviate the requirements for double-strand breaks and homology-directed repair.