  We present a numerical solution in the form of a three-dimensional (3D)
vortex soliton in unmagnetized plasma in the model of the generalized Zakharov
equations with saturating exponential nonlinearity. To find the solution with a
high accuracy we use two-step numerical method combining the Petviashvili
iteration procedure and the Newton-Kantorovich method. The vortex soliton with
the topological charge $m=1$ turns out to be stable provided the nonlinear
frequency shift exceeds a certain critical value. The stability predictions are
verified by direct simulations of the full dynamical equation.
