Using phase-modulation-induced potential gradient whose period is synchronized to a microwave opto-electronic oscillator, dissipative Kerr solitons generated in a crystalline optical microresonator are trapped by the soliton tweezing effect, exhibiting a stabilized soliton repetition rate. In the meantime, side-mode suppression of the microwave signal is enabled by the photodetection of the soliton train. Substantiated both experimentally and theoretically, the hybrid system produces a drift-reduced microcomb and a spectrum-purified optoelectronic oscillator simultaneously, yielding a low-cost toolkit for microwave and optical metrology.