We report on a measurement of CP-violating asymmetries (A(CP)) in the Cabibbo-suppressed D-0 -> pi(+) pi(-) and D-0 -> K+ K- decays reconstructed in a data sample corresponding to 5.9 fb(-1) of integrated luminosity collected by the upgraded Collider Detector at Fermilab. We use the strong decay D*(+) -> D-0 pi(+) to identify the flavor of the charmed meson at production and exploit CP-conserving strong c (c) over bar pair production in p (p) over bar collisions. High-statistics samples of Cabibbo-favored D-0 -> K- pi(+) decays with and without a D*(+/-) tag are used to correct for instrumental effects and significantly reduce systematic uncertainties. We measure A(CP)(D-0 -> pi(+) pi(-)) = (+0.22 +/- 0.24(stat) +/- 0.11(syst))% and A(CP)(D-0 -> K+K-) = (-0.24 +/- 0.22(stat) +/- 0.09(syst))%, in agreement with CP conservation. These are the most precise determinations from a single experiment to date. Under the assumption of negligible direct CP violation in D-0 -> pi(+) pi(-) and D-0 -> K+ K- decays, the results provide an upper limit to the CP-violating asymmetry in D-0 mixing,vertical bar A(CP)(ind)(D-0)vertical bar < 0.13% at the 90% confidence level. RI St.Denis, Richard/C-8997-2012; Robson, Aidan/G-1087-2011; Prokoshin, Fedor/E-2795-2012; maestro, paolo/E-3280-2010; song, hao/I-2782-2012