The photon spectrum from free-electron laser (FEL) light sources offers valuable information in time-resolved experiments and machine optimization in the spectral and temporal domains. We have developed a compact single-shot photon spectrometer to diagnose soft X-ray spectra. The spectrometer consists of an array of off-axis Fresnel zone plates (FZP) that act as transmission-imaging gratings, a Ce:YAG scintillator, and a microscope objective to image the scintillation target onto a two-dimensional imaging detector. This spectrometer operates in segmented energy ranges which covers tens of electronvolts for each absorption edge associated with several atomic constituents: carbon, nitrogen, oxygen, and neon. The spectrometer's performance is demonstrated at a repetition rate of 120 Hz, but our detection scheme can be easily extended to 200 kHz spectral collection by employing a fast complementary metal oxide semiconductor (CMOS) line-scan camera to detect the light from the scintillator. This compact photon spectrometer provides an opportunity for monitoring the spectrum downstream of an endstation in a limited space environment with sub-electronvolt energy resolution.