Abstract Predicting plant distributions under climate change is constrained by our limited understanding of potential rapid adaptive evolution. In an experimental evolution study with the invasive common ragweed ( Ambrosia artemisiifolia L.) we subjected replicated populations of the same initial genetic composition to simulated climate warming. Pooled DNA sequencing of parental and offspring populations showed that warming populations experienced greater genetic divergence from their parents, than control populations. In a common environment, offspring from warming populations showed more convergent phenotypes in seven out of nine plant traits, with later flowering and larger biomass, than plants from control populations. For both traits, we also found a significantly higher ratio of phenotypic to genetic differentiation across generations for warming than for control populations, indicating stronger response to selection under warming conditions. As a measure for evolutionary rate, the phenotypic and sequence divergence between generations were assessed using the Haldane metric. Our approach combining comparisons between generations (allochronic) and between treatments (synchronic) in an experimental evolutionary field study, and linking population genomic data with phenotyping analyses provided a powerful test to detect rapid responses to selection. Our findings demonstrate that ragweed populations can rapidly evolve in response to climate change within a single generation. Short‐term evolutionary responses to climate change may aggravate the impact of some plant invaders in the future and should be considered when making predictions about future distributions and impacts of plant invaders.