The S.I unit of relative density is "has no S.I unit."
Relative density, also known as specific gravity, is the ratio of the density of a substance to the density of a reference substance, usually water. Since it is a ratio of two quantities with the same unit, it does not have a unit itself. Therefore, relative density has no S.I unit.
For example, if the density of a substance is 5 g/cm^3 and the density of water is 1 g/cm^3, then the relative density of the substance is 5/1 = 5. Note that the units of both densities cancel out, leaving a dimensionless quantity.
In summary, relative density is a dimensionless quantity, which means it has no S.I unit.