We numerically investigate the contribution of the microstreaming to the acoustic radiation force acting on a small elastic spherical particle placed into an ultrasonic standing wave. When an acoustic wave scatters on a particle the acoustic radiation force and the microstreaming appear as nonlinear time-averaged effects. The compressible Navier-Stokes equations are solved up to second order in terms of the small Mach number using a finite element method. We show that when the viscous boundary layer thickness to particle radius ratio is sufficiently large and the particle is sufficiently dense, the acoustic microstreaming dominates the acoustic radiation force. In this case, our theory predicts migration of the particle to the velocity node (pressure antinode).