Photonic integrated circuits (PICs) can drastically expand the capabilities of quantum and classical optical information science and engineering. PICs are commonly fabricated using selective material etching, a subtractive process. Thus, the chip's functionality cannot be substantially altered once fabricated. Here, we propose to exploit wide-bandgap non-volatile phase-change materials (PCMs) to create rewritable PICs. A PCM-based PIC can be written using a nanosecond pulsed laser without removing any material, akin to rewritable compact disks. The whole circuit can then be erased by heating, and a new circuit can be rewritten. We designed a dielectric-assisted PCM waveguide consisting of a thick dielectric layer on top of a thin layer of wide-bandgap PCMs Sb2S3 and Sb2Se3. The low-loss PCMs and our designed waveguides lead to negligible optical loss. Furthermore, we analyzed the spatiotemporal laser pulse shape to write the PICs. Our proposed platform will enable low-cost manufacturing and have a far-reaching impact on the rapid prototyping of PICs, validation of new designs, and photonic education.