Methods for rapidly assessing sequence-structure-function landscapes and developing conditional gene-regulatory devices are critical to our ability to manipulate and interface with biology. We describe a framework for engineering RNA devices from preexisting aptamers that exhibit ligand-responsive ribozyme tertiary interactions. Our methodology utilizes cell sorting, high-throughput sequencing and statistical data analyses to enable parallel measurements of the activities of hundreds of thousands of sequences from RNA device libraries in the absence and presence of ligands. Our tertiary-interaction RNA devices performed better in terms of gene silencing, activation ratio and ligand sensitivity than optimized RNA devices that rely on secondary-structure changes. We applied our method to build biosensors for diverse ligands and determine consensus sequences that enable ligand-responsive tertiary interactions. These methods advance our ability to develop broadly applicable genetic tools and to elucidate the underlying sequence-structure-function relationships that empower rational design of complex biomolecules.