We propose a consensus method for ancestral recombination graphs (ARGs) that generates a single ARG representing commonalities among a cloud of ARGs defined for the same genomic region and set of taxa. Our method, which we call “threshold consensus,” treats a genomic location as a potential recombination breakpoint only if the number of ARGs in the cloud possessing a breakpoint at that location exceeds a chosen threshold. The estimate is further refined by ignoring recombinations that do not change the local tree topologies, as well as collapsing breakpoint locations separated only by invariant sites. We test the threshold consensus algorithm, using a range of threshold values, on simulated ARGs inferred by a genealogy sampling algorithm, and evaluate accuracy of breakpoints and local topologies in the resulting consensus ARGs.