Photonic integrated circuits (PICs) demand tailored spectral responses for various applications. On-chip Bragg filters offer a promising solution, yet their static nature hampers scalability. Current tunable filters rely on volatile switching mechanisms plagued by high static power consumption and thermal crosstalk. Here, we introduce, for the first time, a non-volatile, electrically programmable on-chip Bragg filter. This device incorporates a nanoscale layer of wide-bandgap phase change material (Sb2S3) atop a periodically structured silicon waveguide. The reversible phase transitions and drastic refractive index modulation of Sb2S3 enable dynamic spectral tuning via foundry-compatible microheaters. Our design surpasses traditional passive Bragg gratings and active volatile filters by offering electrically controlled, reconfigurable spectral responses in a non-volatile manner. The proposed filter achieves a peak reflectivity exceeding 99% and a high tuning range ($\Delta\lambda$=20 nm) when transitioning between the amorphous and crystalline states of Sb2S3. Additionally, we demonstrate quasi-continuous spectral control of the filter stopband by modulating the amorphous/crystalline distribution within Sb2S3. Our approach offers substantial benefits for low-power, programmable PICs, thereby laying the groundwork for prospective applications in optical communications, optical interconnects, microwave photonics, optical signal processing, and adaptive multi-parameter sensing.