The fast Fourier Transform (FFT), a reduced-complexity formulation of the Discrete Fourier Transform (DFT), is an important tool in many areas of science and engineering. FFTW is a well-known package that follows this approach and is currently one of the fastest available implementations of the FFT. NVIDIA introduced its version of FFTW called cuFFT that achieves high performance on the GPUs. In this work we present a novel way to map the FFT algorithm on the newly introduced Tensor Cores by adapting the the Cooley-Tukey recursive FFT algorithm. We present four major types of optimizations that enhance the performance of our approach for varying FFT sizes and show that the approach consistently outperforms cuFFT with a speedup of about 15% to 250% on average.