For the search for scalar leptons in the minimal supersymmetric standard model (MSSM) as well as for future precision analyses of these particles an accurate knowledge of their production and decay properties is mandatory. We evaluate the cross sections for the slepton production at e+e- colliders in the MSSM with complex parameters (cMSSM). The evaluation is based on a full one-loop calculation of the production mechanisms e+e-→l~gsl~gs′ including soft and hard photon radiation. The dependence of the slepton production cross sections on the relevant cMSSM parameters is analyzed numerically. We find sizable contributions to many production cross sections. They amount to roughly 15% of the tree-level results but can go up to 40% or higher in extreme cases. Also the dependence on complex parameters of the one-loop corrections for the production of charged sleptons was found non-negligible. The full one-loop contributions are thus crucial for physics analyses at a future linear e+e- collider such as the ILC or CLIC.