Three dimensional (3D) topological insulators display an array of unique properties such as single Dirac-cone surface states and a strong magnetoelectric effect. Here we show how a 3D topological spectrum can be induced in a trivial insulator by a periodic drive and, in particular, using electromagnetic radiation. In contrast to the two-dimensional analog, we show that a two-photon resonance is required to transform an initially unremarkable band structure into a topological Floquet spectrum. We provide an intuitive, geometrical picture, alongside a numerical solution of a driven lattice model featuring a single surface Dirac mode. Also, we show that the polarization and frequency of the driving electromagnetic field control the details of the surface modes and particularly the Dirac mass. Specific experimental realizations of the 3D Floquet topological insulator are proposed.