The Ma_MISS spectrometer is integrated within the drilling system of the Rosalind Franklin ExoMars rover. This paper reports the on-ground calibration campaign performed on the spectrometer. Here, we focus on the spectral calibration of the instrument. The experimental setup used to carry out calibration is described, and the methods used for data processing and key parameters retrieval are explained. In particular, the spectral parameters such as (i) pixel central wavelengths, (ii) spectral response function, (iii) spectral resolution, (iv) sampling, and (v) range are determined. In a follow-up paper, the linearity and radiometric calibrations are described, while in De Sanctis et al. [Planet. Sci. J. 3, 142 (2022)], the validation of spectral measurements performed on synthetic and natural rock targets is presented.