Soil organic carbon (SOC) sequestration is the transfer and storage of atmospheric carbon dioxide in soils, which plays an important role in climate change mitigation. SOC concentration can be improved by proper land use, thus it is beneficial if SOC can be estimated at a regional or global scale. As multispectral satellite data can provide SOC-related information such as vegetation and soil properties at a global scale, estimation of SOC through satellite data has been explored as an alternative to manual soil sampling. Although existing works show promising results, most studies are based on pixel-based approaches with traditional machine learning methods, and convolutional neural networks (CNNs) are seldom used. To study the advantages of using CNNs on SOC remote sensing, in this paper, we propose the FNO-DenseNet based on the state-of-the-art Fourier neural operator (FNO). By combining the advantages of the FNO and DenseNet, the FNO-DenseNet outperformed the FNO in our experiments with hundreds of times fewer parameters. The FNO-DenseNet also outperformed a pixel-based random forest by 18% in the mean absolute percentage error. To the best of our knowledge, this is the first work of applying the FNO on SOC remote sensing.