The present study investigates the I-V and spin-transport characteristics of a side-coupled graphene nano-ring. Where, non-equilibrium Green's function approach has been employed as computational framework. Meanwhile the effect of substrate induced Rashba interaction has been considered as a source of spin-dependent processes in the transport phenomena. Calculations have been performed within the coherent regime in which the electric and spin currents of the system are given as a function of bias voltage and Rashba coupling strength. Results show that Aharonov-Bohm oscillations and Fano factor could be changed by the Rashba coupling strength. The Rashba interaction can change the Fano factor from the Poisson to sub-Poisson regime in the case of armchair leads.