  We show that the intrinsic chiral $d_{x^2-y^2} \pm id_{xy}$-wave
superconducting pairing in doped graphene is significantly strengthened in the
core region of a doubly quantized s-wave superconducting vortex produced in a
graphene-superconductor hybrid structure. The chiral d-wave state is induced by
proximity effect, which transfers the center-of-mass angular momentum of the
s-wave vortex to the orbital angular momentum of the chiral d-wave Cooper
pairs. The proximity effect is enhanced by the circular geometry of the vortex
and we find a $[1 + (T-T_{c,J})^2]^{-1}$ temperature dependence for the chiral
d-wave core amplitude, where $T_{c,J}$ is its intrinsic bulk transition
temperature. We further propose to detect the chiral d-wave state by studying
the temperature dependence of the low-energy local density of states in the
vortex core, which displays a sudden radial change as function of the strength
of the d-wave core state.
