Rapid prototyping of interactive textiles is still challenging, since manual skills, several processing steps, and expert knowledge are involved. We present Rapid Iron-On User Interfaces, a novel fabrication approach for empowering designers and makers to enhance fabrics with interactive functionalities. It builds on heat-activated adhesive materials consisting of smart textiles and printed electronics, which can be flexibly ironed onto the fabric to create custom interface functionality. To support rapid fabrication in a sketching-like fashion, we developed a handheld dispenser tool for directly applying continuous functional tapes of desired length as well as discrete patches. We introduce versatile compositions techniques that allow for creating complex circuits, utilizing commodity textile accessories and sketching custom-shaped I/O modules. We further contribute a comprehensive library of components for input, output, wiring and computing. Three example applications, results from technical experiments and expert reviews demonstrate the functionality, versatility and potential of this approach.