Multi-core systems are required by digital signal processors (DSP) to support the revolutionary Multiple-Input Multiple-Output (MIMO) imaging radars in the automotive industry. Such multi-core processors for Frequency Modulated Continuous Wave (FMCW) radars require the use of low- footprint accelerators that would reduce the overhead as the system scales up with the antenna density. In this paper, we propose an FFT accelerator, named RbFFT, optimized for the MIMO radar processing chain. The architecture of RbFFT reduces the overhead by re-using existing memory in the processing element (PE), and employs a dual-radix butterfly engine with mixed bit resolution to optimize resources in dense radars. RbFFT reduces area by implementing for the first time ultra-low compression in its dual twiddle factor ROM. RbFFT also innovates with custom fetching and buffering strategies to improve memory-based FFTs while reusing logic to integrate reverse bit ordering, windowing and inverse FFT (IFFT) within the same accelerator passes. The proposed accelerator is implemented in a 25-Core Smart MPSoC in 22FDX using Adaptive Body Biasing (ABB) at 0.6V. Besides RbFFT being pioneer in specialized FFT accelerators for dense MIMO systems, the results also show state-of-the-art improvements via 11% reduction in the normalized energy consumption, 4% reduction in latency, and 11 times area reduction with relation to previous silicon implementations.