[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.
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