We study the self-focusing and defocusing of a light beam carrying angular momentum (called twisted light) propagating in a nonlinear medium. We derive a differential equation for the beam width parameter f as a function of the propagation distance, angular frequency, beam waist and intensity of the beam. The method is based on the Wentzel-Kramers-Brillouin and the paraxial approximations. Analytical expressions for f are obtained, analyzed and illustrated for typical experimental situations.