The rapid pace of contemporary environmental change puts many species at risk, especially rare species constrained by limited capacity to adapt or migrate due to low genetic diversity and/or fitness. But the ability to acclimate can provide another way to persist through change. We compared the capacity of rare Boechera perstellata (Braun's rockcress) and widespread B. laevigata to acclimate to change. We investigated the phenotypic plasticity of growth, biomass allocation, and leaf morphology of individuals of B. perstellata and B. laevigata propagated from seed collected from several populations throughout their ranges in a growth chamber experiment to assess their capacity to acclimate. Concurrently, we assessed the genetic diversity of sampled populations using 17 microsatellite loci to assess evolutionary potential. Plasticity was limited in both rare B. perstellata and widespread B. laevigata, but differences in the plasticity of root traits between species suggest that B. perstellata may have less capacity to acclimate to change. In contrast to its widespread congener, B. perstellata exhibited no plasticity in response to temperature and weaker plastic responses to water availability. As expected, B. perstellata also had lower levels of observed heterozygosity than B. laevigata at the species level, but population‐level trends in diversity measures were inconsistent due to high heterogeneity among B. laevigata populations. Overall, the ability of phenotypic plasticity to broadly explain the rarity of B. perstellata versus commonness of B. laevigata is limited. However, some contextual aspects of our plasticity findings compared with its relatively low genetic variability may shed light on the narrow range and habitat associations of B. perstellata and suggest its vulnerability to climate warming due to acclimatory and evolutionary constraints.