Solution-processed polymer nanodiodes operating at frequencies up to 20 MHz are demonstrated. As the active layer, p-type semiconductor poly(didodecylquarterthiophene) (PQT12) was used. It is shown that devices based on linear arrays of semiconducting polymer nanowires with intentionally broken symmetry display nonlinear current-voltage characteristics similar to conventional diodes. The so-called self-switching devices (SSDs) are single layered, planar structures that can be easily fabricated in a single step of nanolithography. The SSDs possess substantially lower parasitic capacitance between contacts than conventional organic diodes and organic thin-film transistors, and we show that the nano-rectifiers can operate at frequencies well above both 125/134 kHz and 13.56 MHz RFID communication bands.