A setup for dispersive X-ray absorption spectroscopy (XAS), employing a new reference scheme, has been implemented and tested at the soft X-ray free-electron laser (FEL) FLASH in Hamburg. A transmission grating was used to split the FEL beam into two copies (signal and reference). The spectral content of both beams was simultaneously measured for intensity normalization within the FEL bandwidth on a shot-to-shot basis. Excellent correlation between the two beams was demonstrated within a few percent for single bunch operation at 143 eV photon energy. Applying the normalization scheme, an absorption spectrum of a Gd2O3thin film sample was recorded around the Gd N4,5-edge photon energy of 143 eV, showing excellent agreement with a reference spectrum measured at a synchrotron. This scheme opens the door for time-resolved single-shot XAS with femtosecond time resolution at FELs.