Numerical simulation of the acoustic agglomeration of micron-sized aerosol particles by a discrete element method (DEM) is demonstrated. The conventional DEM technique used in granular dynamics is modified for simulation of the acoustically induced attractive motion of particles in an incompressible fluid. The problem-specific orthokinetic collision, acoustic wake, and mutual radiation pressure effects yielding binary attraction and sticking of the particles are considered within the DEM approach. The acoustically induced agglomeration of two aerosol particles and 3D particles' system is illustrated by numerical results. Numerical values of the agglomeration time of two particles obtained for a wide range of acoustic frequencies are analyzed. Comparison of various hydrodynamic effects with available experimental data indicates an overestimated contribution of the mutual radiation pressure model. The performance of the DEM technique and specific features concerning long-range interactions between particles are demonstrated by simulating 3D particles' systems. The obtained numerical results illustrating the variation of number concentration with time are compared to available experimental data of coal-fired fly ash particles' agglomeration; a relatively good agreement with the acoustic wake mechanism is observed.