On-demand droplet generation with tunable droplet volume is fundamental in many droplet microfluidic applications. In this work, we propose an acoustofluidic method to produce water-in-oil droplets with prescribed volume in an on-demand manner. Surface acoustic waves produced from a slanted interdigital transducer are coupled with parallel laminar streams of dispersed and continuous phase fluids. Acoustic radiation force acting on the fluid interface enable generation of droplets in a microfluidic chip. We expect that the proposed acoustofluidic droplet generation method will serve as a promising tool for on-demand droplet generation with on-chip droplet volume control.