Precise control over droplet position within a microchannel is fundamental to droplet microfluidic applications. This article proposes acoustothermal tweezer for the control of droplet position, which is based on thermocapillary droplet migration actuated by acoustothermal heating. The proposed system comprises an acoustothermal heater, which is composed of a slanted finger interdigital transducer patterned on a piezoelectric substrate and a thin PDMS membrane, and a PDMS microchannel. In the proposed system, droplets moving in a droplet microfluidic chip experience spatiotemporally varying thermal stimuli produced by acoustothermal heating and thus migrate laterally. In comparison to previous methods for droplet sorting, the acoustothermal tweezer offers significant advantages: first, the droplet position can be manipulated in two opposite directions, which enables bidirectional droplet sorting to one of three outlets downstream; second, precise control over the droplet position as well as improved droplet lateral displacement on the order of hundreds of micrometers can be achieved in a deterministic manner, thereby enabling multichannel droplet sorting; third, the PDMS microfluidic chip is disposable and thus can be easily replaced since it is attached to the substrate by reversible bonding, which allows the acoustothermal heater to be reused. Given these advantages, the proposed droplet sorting system is a promising droplet microfluidic lab-on-a-chip platform for tunable, on-demand droplet position control.