The B-+/- meson production asymmetry in pp collisions is measured using B-+/- -> (D) over bar (0)pi(+) decays. The data were recorded by the LHCb experiment during Run 1 of the LHC at center- of- mass energies of ffiffiffi root s = 7 and 8 TeV. The production asymmetries, integrated over transverse momenta in the range 2 < p(T) < 30 GeV/c, and rapidities in the range 2.1 < y < 4.5 are measured to be A(prod)(B+, root s = 7 TeV) = (-0.41 +/- 0.49 +/- 0.10) x 10(- 2), A(prod)(B+, root s = 8 TeV = (- 0.53 +/- 0.31 +/- 0.10) x 10(-2), where the first uncertainties are statistical and the second are systematic. These production asymmetries are used to correct the raw asymmetries of (B+ -> J/psi K+) decays, thus allowing a measurement of the CP asymmetry, A(CP)(B+-> J/psi K+) = (0.09 +/- 0.27 +/- 0.07) x 10(-2)