Allosteric transcription factors (aTF), widely used as biosensors, have proven challenging to design for detecting novel molecules because mutation of ligand-binding residues often disrupts allostery. We developed Sensor-seq, a high-throughput platform to design and identify aTF biosensors that bind to non-native ligands. We screened a library of 17,737 variants of the aTF TtgR, a regulator of a multidrug exporter, against six non-native ligands of diverse chemical structures - four derivatives of the cancer therapeutic tamoxifen, the antimalarial drug quinine, and the opiate analog naltrexone - as well as two native flavonoid ligands, naringenin and phloretin. Sensor-seq identified novel biosensors for each of these ligands with high dynamic range and diverse specificity profiles. The structure of a naltrexone-bound design showed shape-complementary methionine-aromatic interactions driving ligand specificity. To demonstrate practical utility, we developed cell-free detection systems for naltrexone and quinine. Sensor-seq enables rapid, scalable design of new biosensors, overcoming constraints of natural biosensors.