We demonstrate radio-frequency tuning of the energy of individual CdTe/ZnTe quantum dots (QDs) by Surface Acoustic Waves (SAWs). Despite the very weak piezoelectric coefficient of ZnTe, SAW in the GHz range can be launched on a ZnTe surface using interdigitated transducers deposited on a c-axis oriented ZnO layer grown on ZnTe containing CdTe QDs. The photoluminescence (PL) of individual QDs is used as a nanometer-scale sensor of the acoustic strain field. The energy of QDs is modulated by SAW in the GHz range and leads to characteristic broadening of time-integrated PL spectra. The dynamic modulation of the QD PL energy can also be detected in the time domain using phase-locked time domain spectroscopy. This technique is in particular used for monitoring complex local acoustic fields resulting from the superposition of two or more SAW pulses in a cavity. Under magnetic field, the dynamic spectral tuning of a single QD by SAW can be used to generate single photons with alternating circular polarization controlled in the GHz range.