In this paper, we propose a range-Doppler algorithm (RDA)-based synthetic aperture radar (SAR) processor for real-time SAR imaging and present FPGA-based implementation results. The processing steps for the RDA include range compression, range cell migration correction (RCMC), and azimuth compression. A matched filtering unit (MFU) and an RCMC processing unit (RPU) are required for real-time processing. Therefore, the proposed RDA-based SAR processor contains an MFU that uses the mixed-radix multi-path delay commutator (MRMDC) FFT and an RPU. The MFU reduces the memory requirements by applying a decimation-in-frequency (DIF) FFT and decimation-in-time (DIT) IFFT. The RPU provides a variable tap size and variable interpolation kernel. In addition, the MFU and RPU are designed to enable parallel processing of four 32-bit which are transferred via a 128-bit AXI bus. The proposed RDA-based SAR processor was designed using Verilog-HDL and implemented in a Xilinx UltraScale+ MPSoC FPGA device. After comparing the execution time taken by the proposed SAR processor with that taken by an ARM cortex-A53 microprocessor, we observed a 85-fold speedup for a 2048 × 2048 pixel image. A performance evaluation based on related studies indicated that the proposed processor achieved an execution time that was approximately 6.5 times less than those of previous FPGA implementations of RDA processors.