Due to their unique properties, magnetic nanoparticles, often made of iron oxides, have received significant attention in chemistry, solid state physics, and the life sciences. Although a magnetic field is the most obvious mean by which one can manipulate magnetic nanoparticles, we here demonstrate that magnetic nanoparticles can be individually controlled by optical manipulation. We quantify the interaction of optically trapped individual magnetic nanoparticles with the electrical field by determining the spring constant. Also, by finite element modeling we determine the extinction, scattering and absorption cross sections of magnetic nanoparticles as well as the real and imaginary parts of their complex polarizability. In comparison to magnetic manipulation, optical manipulation has the advantage, due to the tight focusing of the laser beam, that it allows for manipulation of a single particle at a time. Also, one can imagine applications where it is advantageous to employ both magnetic and optical manipulations simultaneously.