Structural rearrangements, including copy-number alterations and inversions, are increasingly recognized as an important contributor to human genetic variation. Copy number variants are readily measured via array-based techniques like comparative genomic hybridization, but copy-neutral variants such as inversion polymorphisms remain difficult to identify without whole genome sequencing. We introduce a method to identify inversion polymorphisms and estimate their frequency in a population using readily available single nucleotide polymorphism (SNP) data. Our method uses a probabilistic model to describe a population as a mixture of forward and inverted chromosomes and identifies putative inversions by characteristic differences in haplotype frequencies around inversion breakpoints. On simulated data, our method accurately predicts inversions with frequencies as low as 25% in the population and reliably estimates inversion frequencies over a wide range. On the human HapMap Phase 2 data, we predict between 88 and 142 inversion polymorphisms with frequency ranging from 20 to 92 percent. Many of these correspond to known inversions or have other evidence supporting them, and the predicted inversion frequencies largely agree with the limited information presently available.