Can I use my contact lens prescription to order new eyeglasses?

No, because often the prescribed power is different for a contact lens and eyeglass lens. This is because the power changes due to the difference in the distance that the lens sets from the eye. The contact floats on the tear layer. The eyeglass lens is held by the frame some distance from the eye. Therefore the power is different between the contact and spectacle lens even though the effective correction is the same.