A theory of the filamentation of high-frequency electromagnetic radiation i
n a plasma with ion acoustic turbulence is developed. The threshold radiati
on flux density required to drive filamentation is determined under conditi
ons such that the squared filament size is larger than the product of the e
lectron-electron mean free path and the mean free path of the electrons wit
h respect to their scattering by turbulent fluctuations of the charge densi
ty. The radiation flux densities required to drive filamentation in a turbu
lent plasma are shown to be lower than those in a laminar plasma. The absol
ute value of the threshold radiation flux density is found to be very sensi
tive to the angle between the wave vector of filamentary perturbations and
the anisotropy axis of turbulent noises.