The vortex coronagraph (VC) is a new generation small inner working angle (IWA) coronagraph currently offered on various 8 m class ground-based telescopes. On these observing platforms, the current level of performance is not limited by the intrinsic properties of actual vortex devices, but by wavefront control residuals and incoherent background (e. g., thermal emission of the sky), or the light diffracted by the imprint of the secondary mirror and support structures on the telescope pupil. In the particular case of unfriendly apertures (mainly large central obscuration) when very high contrast is needed (e. g., direct imaging of older exoplanets with extremely large telescopes or space-based coronagraphs), a simple VC, like most coronagraphs, cannot deliver its nominal performance because of the contamination due to the diffraction from the obscured part of the pupil. Here, we propose a novel yet simple concept that circumvents this problem. We combine a vortex phase mask in the image plane of a high-contrast instrument with a single pupil-based amplitude ring apodizer, tailor-made to exploit the unique convolution properties of the VC at the Lyot-stop plane. We show that such a ring-apodized vortex coronagraph (RAVC) restores the perfect attenuation property of the VC regardless of the size of the central obscuration, and for any (even) topological charge of the vortex. More importantly, the RAVC maintains the IWA and conserves a fairly high throughput, which are signature properties of the VC.