Short tandem repeats (STRs) are involved in dozens of Mendelian disorders and have been implicated in complex traits. However, genotyping arrays used in genome-wide association studies focus on single nucleotide polymorphisms (SNPs) and do not readily allow identification of STR associations. We leverage next-generation sequencing (NGS) from 479 families to create a SNP + STR reference haplotype panel. Our panel enables imputing STR genotypes into SNP array data when NGS is not available for directly genotyping STRs. Imputed genotypes achieve mean concordance of 97% with observed genotypes in an external dataset compared to 71% expected under a naive model. Performance varies widely across STRs, with near perfect concordance at bi-allelic STRs vs. 70% at highly polymorphic repeats. Imputation increases power over individual SNPs to detect STR associations with gene expression. Imputing STRs into existing SNP datasets will enable the first large-scale STR association studies across a range of complex traits.