  We present a uniqueness result in dimensions $2$ and $3$ for the inverse
fixed angle scattering problem associated to the Schr\"odinger operator
$-\Delta+q$, where $q$ is a small real valued potential with compact support in
the Sobolev space $W^{\beta,2}$ with $\beta>0.$
  This result improves the known result, due to Stefanov, in the sense that
almost no regularity is required for the potential.
  The uniqueness result still holds in dimension $4$, but for more regular
potentials in $W^{\beta,2}$ with $\beta>2/3$.
