The sources which reionized the intergalactic medium by redshift ̃6 are still unknown. A severe constraint on the ionization process is the low emissivity required to maintain the ionization in the Lya forest. Simulation-calibrated observations suggest a production rate of at most only a few photons per baryon. In this work, we present a new solution to this 'photonstarvation' problem using a weak background of cosmic magnetic fields, which may be present as a consequence of early-Universe physics and subsequent magneto-hydrodynamical amplification. If present, such magnetic fields can induce density perturbations which are dominant on scales comparable to those probed by measurements of hydrogen-absorption lines at redshifts z ̃ 2-5. We show that a subnanoGauss magnetic field, coherent on scale ̃1Mpc with an almost scale-invariant spectrum, is sufficient to produce significant impact on the effective optical depth, the appearance of the Lyα forest on quasar spectra, the pixel-flux statistics and the power spectrum of transmitted flux. We also show that such magnetic field signatures are effectively erased when the metagalactic photoionization rate is increased, hence relaxing the constraint on the cosmic photon budget available for reionization. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.