The asymmetry in the production cross-section @s of D^+/- mesons,A_P=@s(D^+)-@s(D^-)@s(D^+)+@s(D^-), is measured in bins of pseudorapidity @h and transverse momentum p_T within the acceptance of the LHCb detector. The result is obtained with a sample of D^+->K_S^0@p^+ 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<@h<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^0@p^+ decay is negligible. No significant dependence on @h or p_T is observed.