  [Abridged] In our previous work on Ark 120, we found that its 2014 X-ray
spectrum is dominated by Comptonisation, while the relativistic reflection
emission only originates at tens of $R_{\rm g}$ from the SMBH. As a result, we
could not constrain the SMBH spin from disc reflection alone. Our aim is to
determine its SMBH spin from an alternative technique based on the global
energetics of the disc-corona system. The spectral analysis uses simultaneous
XMM-Newton (OM and pn) and NuSTAR observations on 2014 March 22 and 2013
February 18. We applied the optxconv model (based on optxagnf) to self
consistently reproduce the emission from the inner corona (warm and hot thermal
Comptonisation) and the outer disc (colour temperature corrected black body),
taking into account both the disc inclination angle and relativistic effects.
We modelled the mild relativistic reflection of the incident Comptonisation
components using the xilconv model. We infer a SMBH spin of
0.83$^{+0.05}_{-0.03}$, adopting the SMBH reverberation mass of
1.50$\times$10$^{8}$ M$_{\odot}$. In addition, we find that the coronal radius
decreases with increasing flux (by about a factor of two), from
85$^{+13}_{-10}$ $R_{\rm g}$ in 2013 to 14$\pm$3 $R_{\rm g}$ in 2014. This is
the first time that such a constraint is obtained for a SMBH spin from this
technique, thanks to the bare properties of Ark 120, its well determined SMBH
mass, and the presence of a mild relativistic reflection component in 2014
which allows us to constrain the disc inclination angle. We caution that these
results depend on the detailed disc-corona structure, which is not yet fully
established. However, the realistic parameter values found suggest that this is
a promising method to determine spin in moderate accretion rate AGN.
