The persistent low-luminosity neutron star X-ray binary 4U 1812-12 is a potential member of the scarce family of ultra-compact systems. We performed deep photometric and spectroscopic optical observations with the 10.4 m Gran Telescopio Canarias in order to investigate the chemical composition of the accreted plasma, which is a proxy for the donor star class. We detect a faint optical counterpart (g ∼ 25, r ∼ 23) that is located in the background of the outskirts of the Sharpless 54 H II region, whose characteristic nebular lines superimpose on the X-ray binary spectrum. Once this is corrected for, the actual source spectrum lacks hydrogen spectral features. In particular, the Hα emission line is not detected, with an upper limit (3σ) on the equivalent width of < 1.3 Å. Helium (He I) lines are also not observed, even though our constraints are not restrictive enough to properly test the presence of this element. We also provide stringent upper limits on the presence of emission lines from other elements, such as C and O, which are typically found in ultra-compact systems with C-O white dwarfs donors. The absence of hydrogen features, the persistent nature of the source at low luminosity, and the low optical-to-X-ray flux ratio confirm 4U 1812-12 as a compelling ultra-compact X-ray binary candidate, for which we tentatively propose a He-rich donor based on the optical spectrum and the detection of short thermonuclear X-ray bursts. In this framework, we discuss the possible orbital period of the system according to disc instability and evolutionary models.