The asymmetry in the production cross-section \sigma of D+/- mesons, A_P = (\sigma(D+) - \sigma(D-))/(\sigma(D+) + \sigma(D-)), is measured in bins of pseudorapidity \eta and transverse momentum p_T within the acceptance of the LHCb detector. The result is obtained with a sample of D+ -> K_S pi+ decays corresponding to an integrated luminosity of 1.0 fb^-1, collected in pp collisions at a centre of mass energy of 7 TeV at the Large Hadron Collider. When integrated over the kinematic range 2.0 < p_T < 18.0 GeV/c and 2.20 < \eta < 4.75, the production asymmetry is A_P = (-0.96+/-0.26+/-0.18)%. The uncertainties quoted are statistical and systematic, respectively. The result assumes that any direct CP violation in the D+ -> K_S pi+ decay is negligible. No significant dependence on \eta or p_T is observed.