We search for CP violation in Cabibbo-suppressed charged D meson decays by measuring the difference between the CP-violating asymmetries for the Cabibbo-suppressed decays D(±)→K(+)K(-)π(±) and the Cabibbo-favored decays D(s)(±)→K(+)K(-)π(±) in the K(+)K(-) mass region of the ϕ resonance. Using 955 fb(-1) of data collected with the Belle detector, we obtain A(CP)(D+→ϕπ+)=(+0.51±0.28±0.05)%. The measurement improves the sensitivity of previous searches by more than a factor of 5. We find no evidence for direct CP violation.