Strong coupling between an atom and an electromagnetic resonator is an important condition in cavity quantum electrodynamics (QED). While strong coupling in various physical systems has been achieved so far, it remained elusive for single atomic ions. In this paper we demonstrate for the first time the coupling of a single ion to an optical cavity with a coupling strength exceeding both atomic and cavity decay rates. We use cavity assisted Raman spectroscopy to precisely characterize the ion-cavity coupling strength and observe a spectrum featuring the normal mode splitting in the cavity transmission due to the ion-cavity interaction. Our work paves the way towards new applications of cavity QED utilizing single trapped ions in the strong coupling regime for quantum optics and quantum technologies.