Photonic generation of radio-frequency signals has shown significant advantages over the electronic counterparts, allowing the high precision generation of radio-frequency carriers up to the terahertz-wave region with flexible bandwidth for radar applications. Great progress has been made in photonics-based radio-frequency waveform generation. However, the approaches that rely on sophisticated benchtop digital microwave components, such as synthesizers and digital-to-analog converters have limited achievable bandwidth and thus resolution for radar detections. Methods based on voltage-controlled analog oscillators exhibit high time-frequency non-linearity, causing degraded sensing precision. Here, we demonstrate, for the first time, a photonic stepped-frequency (SF) waveform generation scheme enabled by MHz electronics with a tunable bandwidth exceeding 30 GHz and intrinsic time-frequency linearity. The ultra-wideband radio-frequency signal generation is enabled by using a polarization-stabilized optical cavity to suppress intra-cavity polarization-dependent instability; meanwhile, the signal's high-linearity is achieved via consecutive MHz acousto-optic frequency-shifting modulation without the necessity of using electro-optic modulators that have bias-drifting issues. We systematically evaluate the system's signal quality and imaging performance in comparison with conventional photonic radar schemes that use high-speed digital electronics, confirming its feasibility and excellent performance for high-resolution radar applications.