Despite much theoretical discussion on the evolutionary significance of intraclonal genetic variation, particularly for modular organisms whose lack of germ‐soma segregation allows for variants arising in clonal growth to contribute to evolutionary change, the potential of this variation to fuel adaptation remains surprisingly untested. Given intraclonal variation, mitotic cell lineages, rather than sexual offspring, may frequently act as units of selection. Here, we applied artificial selection to such lineages in the branching red seaweed Asparagopsis armata, targeting aspects of clonal growth form and growth‐form plasticity that enhance light acquisition on patchy subtidal reefs and predicting that a genetic basis to intraclonal variation may promote significant responses that cannot accompany phenotypic variation alone. Cell‐lineage selection increased variation in branch proliferation among A. armata genets and successfully altered its plasticity to light. Correlated responses in the plasticity of branch elongation, moreover, showed that cell‐lineage selection may be transmitted among the plasticities of growth‐form traits in A. armata via pleiotropy. By demonstrating significant responses to cell‐lineage selection on growth‐form plasticity in this seaweed, our study lends support to the notion that intraclonal genetic variation may potentially help clonal organisms to evolve adaptively in the absence of sex and thereby prove surprisingly resilient to environmental change.