A search for CP violation in Cabibbo-suppressed D ± → K S 0 K ± and D ± → K S 0 π ± decays is performed using pp collision data, corresponding to an integrated luminosity of 3 fb, recorded by the LHCb experiment. The individual CP-violating asymmetries are measured to be $$ \begin{array}{l}{\mathcal{A}}_{CP}^{D\pm}\to {K}_{\mathrm{S}}^0{K}^{\pm }=\left(+0.03\pm 0.17\pm 0.14\right)\%\hfill \\ {}{\mathcal{A}}_{CP}^{D_s^{\pm }}\to {K}_{\mathrm{S}}^0{\pi}^{\pm }=\left(+0.38\pm 0.46\pm 0.17\right)\%,\hfill \end{array} $$ assuming that CP violation in the Cabibbo-favoured decays is negligible. A combination of the measured asymmetries for the four decay modes D () ± → K S 0 K ± and D () ± → K S 0 π ± gives the sum $$ {\mathcal{A}}_{CP}^{D\pm \to {K}_{\mathrm{S}}^0{K}^{\pm }}+{\mathcal{A}}_{CP}^{D_s^{\pm}\to {K}_{\mathrm{S}}^0{\pi}^{\pm }}=\left(+0.41\pm 0.49\pm 0.26\right)\%. $$ In all cases, the first uncertainties are statistical and the second systematic. The results represent the most precise measurements of these asymmetries to date and show no evidence for CP violation.