This paper studies the effect of turbulence on the orbital angular momentum (OAM) of the Laguerre-Gaussian beam propagating through the atmosphere. An integral representation of laser beam OAM through the beam intensity distribution and the gradient of the medium permittivity is derived. The equations are obtained for the first OAM statistical moments: the mean and the mean square. It is shown that the OAM value, averaged over medium realizations, coincides with the OAM value in a homogeneous medium. Asymptotic equations are derived, which allow OAM fluctuations to be estimated under the extreme conditions of weak and strong turbulence, depending on the diffraction parameters of the beam. It is found that the rate of growth of OAM fluctuations increases, as the propagating beam passes from the conditions of weak turbulence to the conditions of strong turbulence.© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.