We calculate the elements of the Stokes matrix for the scattering of light from a one-dimensional, perfectly conducting, randomly rough surface in the general case when the plane of incidence is not perpendicular to the generators of the surface. By using Green's second integral identity we obtain a pair of inhomogeneous integral equations for the surface values of the components of the total electric and magnetic fields in the system parallel to the generators of the surface. All components of the scattered field can be obtained from these two components, and from them the elements of the Stokes matrix can be calculated. These equations are solved numerically for each of 2000 realizations of the surface profile function, and the elements of the Stokes matrix are averaged over this ensemble of realizations of the surface profile function. We find that only four unique elements of the Stokes matrix are nonzero, as in the case in which the plane of incidence is normal to the generators of the surface (in-plane scattering). Moreover, these nonzero elements in the conical scattering of light of wavelength λ can be obtained from the corresponding elements in the in-plane scattering of light of an effective wavelength λeff = λ/ cos ф0, where ф0 is the conical angle. The results of the study enable complete information about the diffuse scattering properties of one-dimensional perfectly conducting random surfaces to be obtained.