Context: The young σ Orionis cluster is an important location for studying the formation and evolution of stars, brown dwarfs, and planetary-mass objects. Its metallicity, although it is a fundamental parameter, has not been well determined yet. Aims: We present the first determination of the metallicity of nine young late-type stars in σ Orionis. Methods: Using the optical and near-infrared broadband photometry available in the literature we derive the effective temperatures for these nine cluster stars, which lie in the interval 4300-6500 K (1-3 {M}_&sun;). These parameters are employed to compute a grid of synthetic spectra based on the code MOOG and Kurucz model atmospheres. We employ a χ^2-minimization procedure to derive the stellar surface gravity and atmospheric abundances of Al, Ca, Si, Fe, Ni and Li, using multi-object optical spectroscopy taken with WYFFOS+AF2 at the William Herschel Telescope (λ/δλ˜7500). Results: The average metallicity of the σ Orionis cluster is [Fe/H] = -0.02±0.09±0.13 (random and systematic errors). The abundances of the other elements, except lithium, seem to be consistent with solar values. Lithium abundances are in agreement with the “cosmic” ^7Li abundance, except for two stars which show a log ɛ(Li) in the range 3.6-3.7 (although almost consistent within the error bars). There are also other two stars with log ɛ(Li)˜ 2.75. We derived an average radial velocity of the σ Orionis cluster of 28±4 km s-1. Conclusions: The σ Orionis metallicity is roughly solar.