Background Single cell Strand-seq is a unique tool for the discovery and phasing of genomic inversions. Conventional methods to discover inversions with Strand-seq data are blind to known inversion locations, limiting their statistical power for the detection of inversions smaller than 10 Kb. Moreover, the methods rely on manual inspection to separate false and true positives. Results Here we describe "InvertypeR", a method based on a Bayesian binomial model that genotypes inversions using fixed genomic coordinates. We validated InvertypeR by re-genotyping inversions reported for three trios by the Human Genome Structural Variation Consortium. Although 6.3% of the family inversion genotypes in the original study showed Mendelian discordance, this was reduced to 0.5% using InvertypeR. By applying InvertypeR to published inversion coordinates and predicted inversion hotspots (n = 3701), as well as coordinates from conventional inversion discovery, we furthermore genotyped 66 inversions not previously reported for the three trios. Conclusions InvertypeR discovers, genotypes, and phases inversions without relying on manual inspection. For greater accessibility, results are presented as phased chromosome ideograms with inversions linked to Strand-seq data in the genome browser. InvertypeR increases the power of Strand-seq for studies on the role of inversions in phenotypic variation, genome instability, and human disease.