The radio galaxy Fornax A (NGC 1316) is a prominent merger remnant in the outskirts of the Fornax cluster. Its giant radio lobes suggest the presence of a powerful AGN and thus a central supermassive black hole (SMBH). We present high-resolution adaptive optics assisted integral-field data of Fornax A, taken with SINFONI at the Very Large Telescope in the K band. We use axisymmetric orbit models to determine the mass of the SMBH in the centre of Fornax A. The three-dimensional nature of our data provides the possibility to directly test the consistency of the data with axisymmetry by modelling each of the four quadrants separately. According to our dynamical models, consistent SMBH masses and dynamical Ks band mass-to-light ratios are obtained for all quadrants, with =1.3x10^8 M_\odot (rms(M_BH)=0.4x10^8 Msun) and =0.68 (rms(M/L)=0.03), confirming the assumption of axisymmetry. For the folded and averaged data we find M_BH=(1.5+0.75-0.8)x10^8 Msun and M/L=(0.65+0.075-0.05) (3-sigma errors). Thus the black-hole mass of Fornax A is consistent within the error with the Tremaine (2002) M-sigma relation, but is a factor ~4 smaller than expected from its bulge mass and the Marconi&Hunt (2003) relation.

24 pages, 24 figures, submitted to MNRAS