  We introduce a new iterative method to recover a real compact supported
potential of the Schr\"odinger operator from their fixed angle scattering data.
The method combines a fixed point argument with a suitable approximation of the
resolvent of the Schr\"odinger operator by partial sums associated to its Born
series. Convergence is established for potentials with small norm in certain
Sobolev spaces. As an application we show some numerical experiments that
illustrate this convergence.
