Einstein's theory of general relativity has been extensively tested in weak gravitational fields, mainly with experiments in the Solar System and observations of radio pulsars, and current data agree well with the theoretical predictions. Nevertheless, there are a number of scenarios beyond Einstein's gravity that have the same predictions for weak fields and present deviations only when gravity becomes strong. Here, we try to test general relativity in the strong field regime. We fit the x-ray spectrum of the supermassive black hole in Ark 564 with a disk reflection model beyond Einstein's gravity, and we are able to constrain the black hole spin a* and the Johannsen deformation parameters α13 and α22 separately. For α22=0 , we find a*>0.96 and -1.0 <α13<0.2 with a 99% confidence level. For α13=0 , we get a*>0.96 and -0.1 <α22<0.9 with a 99% confidence level. Our measurements are, thus, consistent with the hypothesis that the supermassive compact object in Ark 564 can be described by the Kerr metric.