Equivariant categories from categorical group actions on monoidal categories

G-equivariant modular categories provide the input for a standard method to construct 3d homotopy field theories. Virelizier constructed a G-equivariant category from the action of a group G on a Hopf algebra H by Hopf algebra automorphisms. The neutral component of his category is the Drinfeld center of the category of H-modules. We generalize this construction to weak actions of a group G on an arbitrary monoidal category C by (possibly non-strict) monoidal auto-equivalences and obtain a G-equivariant category with neutral component the Drinfeld center of C.