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We measure the dimuon charge asymmetry A in pp̅ collisions at a center of mass energy √s =1960 GeV. The data was recorded with the D0 detector and corresponds to an integrated luminosity of approximately 1:0 fb-1. Assuming that the asymmetry A is due to asymmetric B0 ↔ B̅ mixing and decay, we extract the CP-violation parameter of B0 mixing and decay: [ℜ(∊B0)]/[1+∣∊B0∣2 = (AB0)/4 = -0.0023 ± 0.0011 (stat) ± 0.0008(syst). AB0 is the dimuon charge asymmetry from decays of B0B̅0 pairs. The general case, with CP violation in both B0 and B0s systems, is also considered. Finally we obtain the forward-backward asymmetry that quantifies the tendency of μ+ to go in the proton direction and μ- to go in the antiproton direction. The results are consistent with the standard model and constrain new physics.