A theory of scattering from a weakly fluctuating random medium is formulated in terms of the effect of the background medium on the propagation of the incident and scattered waves. The nonrandom background medium is treated by a rigorous representation for electromagnetic waves interacting with a cylindrically symmetric, radially nonuniform plasma. The resulting boundary value problem is solved numerically using a 50-layered approximation of the radial distribution. The scattering from the turbulent fluctuations, including depolarization effects, is calculated using existing theories that approximate the plasma by a weakly fluctuating refractive index except that the propagation in the background medium determines the local effective wavenumber and the weight factor for local turbulence scattering. This model is in good agreement with published data on microwave scattering from laboratory plasma where the microwaves do not interact with collisionless overdense regions in the plasma because of refractive effects.