  The weak lensing effects are known to change only weakly the shape of the
power spectrum of the Cosmic Microwave Background (CMB) temperature
fluctuations. I show here that they nonetheless induce specific non-Gaussian
effects that can be detectable with the four-point correlation function of the
CMB anisotropies. The magnitude and geometrical dependences of this correlation
function are investigated in detail. It is thus found to scale as the square of
the derivative of the two-point correlation function and as the angular
correlation function of the gravitational displacement field. It also contains
specific dependences on the shape of the quadrangle formed by the four
directions.
  When averaged at a given scale, the four-point function, that identifies with
the connected part of the fourth moment of the probability distribution
function of the local filtered temperature, scales as the square of logarithmic
slope of its second moment, and as the variance of the gravitational
magnification at the same angular scale.
  All these effects have been computed for specific cosmological models. It is
worth noting that, as the amplitude of the gravitational lens effects has a
specific dependence on the cosmological parameters, the detection of the
four-point correlation function could provide precious complementary
constraints to those brought by the temperature power spectrum.
