  We adapt a non-linear filter proposed by Hu 2001 for detecting lensing of the
CMB by large-scale structures to recover surface-density profiles of galaxy
clusters from their localised, weak gravitational lensing effect on CMB fields.
Shifting the band-pass of the filter to smaller scales, and normalising it such
as to reproduce the convergence rather than the deflection angle, we find that
the mean density profile of a sample of 100 clusters can be recovered to better
than 10% from well within the scale radius to almost the virial radius. The
kinetic Sunyaev-Zel'dovich effect is shown to be a negligible source of error.
We test the filter applying it to data simulated using the characteristics of
the Atacama Cosmology Telescope (ACT), showing that it will be possible to
recover mean cluster profiles outside a radius of 1' corresponding to ACT's
angular resolution.
