We present a new approach for electronic control of optical tweezers by using space--time--wavelength mapping (STWM), a technique that uses time--domain modulation to control local intensity values, and hence the resulting optical force, in space. The proposed technique enables direct control of magnitude, location, and polarity of force hot--spots created by Lorentz force (gradient force). In this paper, we develop an analytical formulation of the proposed STWM technique for optical tweezing. In the case study presented here, we show that 150 fs optical pulses are dispersed in time and space to achieve a focused elliptical beam that is ~20 μm long and ~2 μm wide. By choosing the appropriate RF waveform and electro--optic modulator, we can generate multiple hot--spots with >200 pN force per pulse.