In this paper a simple analytic model for deflection of a laser beam in the presence of flowing plasma is presented. The model utilizes a nonlinear solution of the paraxial wave equation in the random phase approximation. This approximation excludes any contribution from hot-spot induced self-focusing, but allows for the effects of intensity fluctuations of the beam. For a speckled beam the solution for the beam intensity in wave number space depends sensitively on the properties of the incident beam. It is shown that for an incident beam whose initial spectrum in wave number space is Gaussian, the final spectrum is also Gaussian with the overall spectrum rotated in wave number space by a radius of curvature function that is an explicit expression of the Mach number of the flow, the local acoustic damping, and the local average intensity. This result is applicable to the case in which the speckle develops upon transmission of the beam through a random phase plate (RPP). The bending rate thus calculated for a RPP-smoothed beam is compared to the bending rate in the absence of the RPP. This comparison provides some insight into the efficacy of the RPP in reducing the bending of the laser beam.