Population scale sequencing of whole human genomes is becoming economically feasible; however, data management and analysis remains a formidable challenge for many research groups. Large sequencing studies, like the 1000 Genomes Project, have improved our understanding of human demography and the effect of rare genetic variation in disease. Variant calling on datasets of hundreds or thousands of genomes is time-consuming, expensive, and not easily reproducible given the myriad components of a variant calling pipeline. Here, we describe a cloud-based pipeline for joint variant calling in large samples using the Real Time Genomics population caller. We deployed the population caller on the Amazon cloud with the DNAnexus platform in order to achieve low-cost variant calling. Using our pipeline, we were able to identify 68.3 million variants in 2,535 samples from Phase 3 of the 1000 Genomes Project. By performing the variant calling in a parallel manner, the data was processed within 5 days at a compute cost of $7.33 per sample (a total cost of $18,590 for completed jobs and $21,805 for all jobs). Analysis of cost dependence and running time on the data size suggests that, given near linear scalability, cloud computing can be a cheap and efficient platform for analyzing even larger sequencing studies in the future.