This research proposes a novel linear frequency modulation (Linear‐FM) random radar waveform and introduces a dechirping compression method. The proposed linear‐FM random waveforms possess a thumbtack ambiguity function and low cross‐correlation properties which are good for fighting against digital radio frequency memory repeat jammer similar to random noise waveforms. The dechirping compression method for the proposed linear‐FM random radar waveform works by mixing the random radar echo signal with a local reference linear frequency modulated (LFM) signal to reduce the echo bandwidth and thus allows to use low‐speed analogue‐to‐digital converter similar to the dechirping method for LFM waveform compression. Both numerical simulation and high‐resolution circular synthetic aperture radar imaging experiment are conducted to demonstrate the good performance of the proposed waveform and the proposed dechirping compression method.