It is of scientific significance to explore the terahertz radiation source with the performances of high power, tunable frequency, and controllable chirp for the realization of coherent control of quantum systems. How to realize frequency chirp control of terahertz synchrotron radiation is the last puzzle to be completed. In this Letter, we propose a method to control the radiation frequency chirp with precision. A novel photomixing scheme is presented to generate a longitudinally modulated laser pulse with non-uniform time intervals between the adjacent micro-peaks, which means that there is a chirp in the modulation frequency, and this chirp can be continuously tuned. The interaction is made to occur between an electron beam and the modulated laser pulse in a modulator (an undulator tuned at the laser wavelength), then terahertz synchrotron radiation with the same spectrum characteristics as the modulated laser will be generated when the electron beam passes through the following bending magnet. We expect that this method will open a new way for the coherent control of quantum systems in the terahertz regime.