Massively parallel, quantitative measurements of biomolecular activity across sequence space can greatly expand our understanding of RNA sequence-function relationships. We report the development of an RNA-array assay to perform such measurements and its application to a model RNA: the core glmS ribozyme riboswitch, which performs a ligand-dependent self-cleavage reaction. We measure the cleavage rates for all possible single and double mutants of this ribozyme across a series of ligand concentrations, determining k_cat and K_M values for active variants. These systematic measurements suggest that evolutionary conservation in the consensus sequence is driven by maintenance of the cleavage rate. Analysis of double-mutant rates and associated mutational interactions produces a structural and functional mapping of the ribozyme sequence, revealing the catalytic consequences of specific tertiary interactions, and allowing us to infer structural rearrangements that permit certain sequence variants to maintain activity.