We study the spin-resolved transport in a two-terminal graphene nanoflake device with a Rashba spin-orbit coupling region in the center of the device. The Green’s function method is applied to the system and the spin transmission probability and the spin polarization in x, y, and z directions are calculated. It is found that the components of the spin polarization are antisymmetric functions of Fermi energy, which oscillate and decay to the zero with increasing the energy for all values of the Rashba strength. It is shown that by tuning the Rashba strength via a gate voltage and/or changing the size of the system, it is possible to control the sign and magnitude of the spin polarization. The system represented here is a typical candidate for full electrical spintronic devices based on the carbon materials that are used for spin filtration.