We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions and additive noise in the vorticity-velocity formulation. The approximation is based on freezing the velocity on time
subintervals resulting in a linear stochastic parabolic equation for vorticity. At each
time step, the velocity is expressed via vorticity using a formula corresponding to
the Biot-Savart-type law. We prove the first mean-square convergence order of the
vorticity approximation.