We report a measurement of the indirect CP-violating asymmetries ($A_{Gamma}$) between effective lifetimes of anticharm and charm mesons reconstructed in $D^0to K^+ K^-$ and $D^0to pi^+pi^-$ 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 $D^{*+}to D^0pi^+$ is used to identify the meson at production as $D^0$ or $overline{D}^0$. We statistically subtract $D^0$ and $overline{D}^0$ mesons originating from $b$-hadron decays and measure the yield asymmetry between anticharm and charm decays as a function of decay time. We measure $A_Gamma (K^+K^-) = (-0.19 pm 0.15 (stat) pm 0.04 (syst))%$ and $A_Gamma (pi^+pi^-)= (-0.01 pm 0.18 (stat) pm 0.03 (syst))%$. The results are consistent with the hypothesis of CP symmetry and their combination yields $A_Gamma = (-0.12 pm 0.12)%$.