  The spacetime geometry around astrophysical black holes is well approximated
by the Kerr metric, but deviations from standard predictions are possible in a
number of scenarios beyond Einstein's gravity and in the presence of exotic
matter. In this paper, we present the constraints on possible deviations from
the Kerr solution using X-ray reflection spectroscopy from the analysis of real
data. We use the relativistic X-ray reflection code RELXILL modified to a
generic stationary, axisymmetric and asymptotically flat black hole metric. We
analyze 350 ks long XMM-Newton observations of the AGN in MCG-06-30-15 taken
during July-August 2001 and constrain the Johannsen deformation parameter
$\alpha_{13}$.
