The quasi-linear theory of a plasma with wave-particle collisions is reconsidered for the case of current-driven ion-acoustic turbulence. Especially the angular dependence of the energy spectrum of the waves is taken into account more accurately in the quasi-linear collision integral. The kinetic equation is solved assuming that the scales of the density gradients of the plasma parallel and perpendicular to an external magnetic field are much larger than the effective mean free path of the electrons. Expressions for the electron diffusion tensor are developed and estimates of the diffusion in solar flare plasmas are made.