Modelling of the weak lensing of the CMB will be crucial to obtain correct cosmological parameter constraints from forthcoming precision CMB anisotropy observations. The lensing affects the power spectrum as well as inducing non-Gaussianities. We discuss the simulation of full sky CMB maps in the weak lensing approximation and describe a fast numerical code. The series expansion in the deflection angle cannot be used to simulate accurate CMB maps, so a pixel remapping must be used. For parameter estimation accounting for the change in the power spectrum but assuming Gaussianity is sufficient to obtain accurate results up to Planck sensitivity using current tools. A fuller analysis may be required to obtain accurate error estimates and for more sensitive observations. We demonstrate a simple full sky simulation and subsequent parameter estimation at Planck-like sensitivity.