Context. The imprint of baryonic acoustic oscillations (BAO) on the matter power spectrum can be constrained using the neutral hydrogen density in the intergalactic medium (IGM) as a tracer of the matter density. One of the goals of the baryon oscillation spectroscopic survey (BOSS) of the Sloan Digital Sky Survey (SDSS-III) is to derive the Hubble expansion rate and the angular scale from the BAO signal in the IGM. To this aim, the Lyman-α forest about 150 000 quasars will be observed in the redshift range 2.2 < z < 3.5 and over ~10 000 deg2. Aims: We simulated the BOSS QSO survey to estimate the statistical accuracy on the BAO scale determination provided by such a large-scale survey. In particular, we discuss the effect of the poorly constrained estimate of the quasar's unabsorbed intrinsic spectrum. Methods: The volume of current N-body simulations being too small for such studies, we resorted to Gaussian random field (GRF) simulations. We validated the use of GRFs by comparing the output of GRF simulations with that of the Horizon-4Π N-body dark-matter-only simulation with the same initial conditions. Realistic mock samples of QSO Lyman-α forest were generated and their power spectrum computed and fitted to obtain the BAO scale. The rms of the results for 100 different simulations provides an estimate of the statistical error expected from the BOSS survey. Results: We confirm the results from the Fisher matrix estimate. In the absence of error on the quasar's unabsorbed spectrum, our simulations give an expected uncertainty of 2.3% for the BOSS quasar survey measurement of the BAO scale. The expected uncertainties for the transverse and radial BAO scales are 6.8% and 3.9%, respectively. The significance of the BAO detection is assessed by an average Δχ2 = 17 but Δχ2 ranges from 2 to 35 for individual realizations. The error on the quasar's unabsorbed spectrum increases the error on the BAO scale by 10 to 20% and results in a subpercent bias.