Rapid spill detection and mapping are needed with increasing levels of oil exploration and production in the Arctic. Previous work has found that ground-penetrating radar (GPR) is effective for qualitative identification of oil spills under, and encapsulated within, sea ice. Quantifying the spill distribution will aid effective spill response. To this end, we have developed a targeted GPR reflection-waveform inversion algorithm to quantify the geometry of oil spills under and within sea ice. With known electric properties of the ice and oil, we have inverted for oil thickness and variations in ice thickness. We have tested the algorithm with data collected during a controlled spill experiment using 500-MHz radar reflection data. The algorithm simultaneously recovered the thickness of a 5-cm-thick oil layer at the base of the ice to within 8% of the control value, estimated the thickness of a 1-cm-thick oil layer encapsulated within the ice to within 30% of the control value, and accurately mapped centimeter-scale variations in ice thickness.