Single-molecule orientation measurements provide unparalleled insight into a multitude of biological and polymeric systems. We report a simple, high-throughput technique for measuring the azimuthal orientation and rotational dynamics of single fluorescent molecules, which is compatible with localization microscopy. Our method involves modulating the polarization of an excitation laser, and analyzing the corresponding intensities emitted by single dye molecules and their modulation amplitudes. To demonstrate our approach, we use intercalating and groove-binding dyes to obtain super-resolved images of stretched DNA strands through binding-induced turn-on of fluorescence. By combining our image data with thousands of dye molecule orientation measurements, we develop a means of probing the structure of individual DNA strands, while also characterizing dye-DNA interactions. This approach may hold promise as a method for monitoring DNA conformation changes resulting from DNA-binding proteins.