Phenotypic plasticity is known to evolve in perturbed habitats, where it alleviates the deleterious effects of selection. But the effects of plasticity on levels of genetic polymorphism, an important precursor to adaptation in temporally varying environments, are unclear. Here we develop a haploid, two-locus population-genetic model to describe the interplay between a plasticity modifier locus and a target locus subject to periodically varying selection. We find that the interplay between these two loci can produce a ‘genomic storage effect’ that promotes balanced polymorphism over a large range of parameters, in the absence of all other conditions known to maintain genetic variation. The genomic storage effect arises as recombination allows alleles at the two loci to escape more harmful genetic backgrounds and associate in haplotypes that persist until environmental conditions change. Using both Monte Carlo simulations and analytical approximations we quantify the strength of the genomic storage effect across a range of selection pressures, recombination rates, plasticity modifier effect sizes, and environmental periods.