We report on optical orientation of singly charged excitons (trions) in charge-tunable self-assembled InAs/GaAs quantum dots. When the charge varies from 0 to -2, the trion photoluminescence of a single quantum dot shows up and under quasiresonant excitation gets progressively polarized from zero to approximately 100%. This behavior is interpreted as the electric control of the trion thermalization process, which subsequently acts on the hole-spin relaxation driven in nanosecond time scale by the anisotropic electron-hole exchange. This is supported by the excitation spectroscopy and time-resolved measurements of a quantum dot ensemble.