  We consider a disordered graphene layer with anisotropic Rashba spin-orbit
coupling subjected to a longitudinal electric field. Using the linear response
theory we calculate current-induced spin polarization including in-plane normal
and parallel components with respect to the electric field direction. Unlike
the case of isotropic Rashba spin-orbit where the normal component of spin
polarization is linear in terms of Fermi energy around the Dirac point,
anisotropic Rashba spin-orbit can result in non-linear dependence of this
component at such energies within the Lifshitz points. Furthermore, we show
that anisotropic Rashba interaction allows for tuning the direction of spin
polarization from perpendicular direction to the parallel one such that for
certain values of Rashba parameters the magnitudes of both components can also
be quenched. The effect of carriers scattering on randomly distributed
non-magnetic disorders is also taken into account by calculating vertex
correction. This results in modification of spin polarization components
depending on the relative strength of Rashba parameters.
