While climate change impacts on crop yields has been extensively studied, estimating the impact of water shortages on irrigated crop yields is challenging because the water resources management system is complex. To investigate this issue, we integrate a crop yield reduction module and a water resources model into the MIT Integrated Global System Modeling framework, an integrated assessment model linking a global economic model to an Earth system model. We assess the effects of climate and socioeconomic changes on water availability for irrigation in the U.S. as well as subsequent impacts on crop yields by 2050, while accounting for climate change projection uncertainty. We find that climate and socioeconomic changes will increase water shortages and strongly reduce irrigated yields for specific crops (i.e., cotton and forage), or in specific regions (i.e., the Southwest) where irrigation is not sustainable. Crop modeling studies that do not represent changes in irrigation availability can thus be misleading. Yet, since the most water-stressed basins represent a relatively small share of U.S. irrigated areas, the overall reduction in U.S. crop yields is small. The response of crop yields to climate change and water stress also suggests that some level of adaptation will be feasible, like relocating croplands to regions with sustainable irrigation or switching to less irrigation intensive crops. Finally, additional simulations show that greenhouse gas (GHG) mitigation can alleviate the effect of water stress on irrigated crop yields, enough to offset the reduced CO2 fertilization effect compared to an unconstrained GHG emission scenario.