We have measured the soft X-ray responsivities of a fully depleted back-illuminated (BI) charge-coupled device (CCD). We constructed a soft X-ray beam line for this purpose and confirmed that we irradiated K lines of carbon, oxygen, and aluminum. We operated the BI CCD in a photon-counting mode with a low-noise condition sufficient to resolve these K lines. We clearly resolved the carbon K line with the BI CCD. Because the mean absorption length of carbon K X-rays is 0.11 µm in silicon, we confirmed that our BI CCD operates in a fully depleted condition. We obtained a good linear relationship between peak pulse height and incident X-ray energy. The energy resolution can be explained by the Fano factor, the readout noise, and a small number of additional unknown noise components.