We reconstruct B±→DK± decays in a data sample collected by the CDF II detector at the Tevatron collider corresponding to 1  fb−1 of integrated luminosity. We select decay modes where the D meson decays to either K−π+ (flavor eigenstate) or K−K+, π−π+ (CP-even eigenstates), and measure the direct CP asymmetry ACP+=0.39±0.17(stat)±0.04(syst), and the double ratio of CP-even to flavor eigenstate branching fractions RCP+=1.30±0.24(stat)±0.12(syst). These measurements will improve the determination of the Cabibbo-Kobayashi-Maskawa angle γ. They are performed here for the first time using data from hadron collisions.