This work is concerned with the wrinkling phenomenon observed in an annular graphene sheet under circular shearing at its inner edge. By performing molecular mechanics simulations on the aforementioned loaded annular graphene sheet, it is observed that the unusual wrinkles formed are confined to within an annulus that hugs the perimeter of the inner radius. This confined wrinkling pattern is in contrast to the wrinkling patterns that spread throughout rectangular graphene sheets under tension or shear. The present wrinkling pattern is characterized by a wave number and wrinkle profile. The wave number at the bifurcation wrinkle is found to depend only on the inner radius of the annular graphene and it increases almost linearly with increasing inner radius. The orientation of these developed waves is found to be at a constant angle and independent from the radii ratio of annular graphene. The wrinkle profile in terms of wave amplitude and wavelength depends on the magnitude of the circular shearing. The predictable formation of wrinkles in annular graphene can be exploited for applications in nano-force sensors, tunable magnetic or electronic devices, as well as patterned stretchable electronics.