Specialized hardware accelerators continue to be a source of performance improvement. However, such specialization comes at a programming price. The fundamental issue is that of a {\em mismatch} between the diversity of user code and the functionality of fixed hardware, limiting its wider uptake. Here we focus on a particular set of accelerators: those for Fast Fourier Transforms. We present FACC (Fourier Accelerator Compiler), a novel approach to automatically map legacy code to Fourier Transform accelerators. It automatically generates drop-in replacement adapters using Input-Output (IO)-based program synthesis that bridge the gap between user code and accelerators. We apply FACC to unmodified GitHub C programs of varying complexity and compare against two existing approaches. We target FACC to a high-performance library, FFTW, and two hardware accelerators, the NXP PowerQuad and the Analog Devices FFTA, and demonstrate mean speedups of 9x, 17x and 27x respectively.