We used the Swarm-C accelerometer data to invert the orbital atmospheric density in this study. First, the Swarm-C satellite mission data were obtained from the ESA’s public data platform, and preliminary data error correction was performed. This paper refers to the calibration method of GRACE-A satellite accelerometer data. It adds linear temperature correction on the original basis. Moreover, this study’s accelerometer data correction results were compared with the data correction results published by the ESA. In order to explore the influence of light radiation on the accelerometer, we established a geometric model of Swarm-C to simulate the physical shape of the satellite surface. The light radiation pressure model and the shadow area judgment model were established, the change in the light radiation acceleration during the transition process of the satellite from the umbra area to the penumbra area and then to the shadowless area was studied, and the state transition during the transition process was analyzed. Finally, the atmospheric drag coefficient was calculated based on the Sentman model. Atmospheric density inversion calculations were performed using the above data. We show the spatial distribution of atmospheric density at a fixed latitude, testing our results during geomagnetic storms. We compared the density results with existing research data, demonstrating the effectiveness of our approach.