We report a measurement of the indirect CP-violating asymmetries (AΓ) between effective lifetimes of anticharm and charm mesons reconstructed in D0→K+K- and D0→π+π- decays. We use the full data set of proton-antiproton collisions collected by the Collider Detector at Fermilab experiment and corresponding to 9.7 fb-1 of integrated luminosity. The strong-interaction decay D*+→D0π+ is used to identify the meson at production as D0 or D¯0. We statistically subtract D0 and D¯0 mesons originating from b-hadron decays and measure the yield asymmetry between anticharm and charm decays as a function of decay time. We measure AΓ(K+K-)=(-0.19±0.15(stat)±0.04(syst))% and AΓ(π+π-)=(-0.01±0.18(stat)±0.03(syst))%. The results are consistent with the hypothesis of CP symmetry and their combination yields AΓ=(-0.12±0.12)%.