We present a new method to measure the polarization state of a terahertz pulse by using a modified electro-optic sampling setup. To illustrate the power of this method, we show two examples in which the knowledge of the polarization of the terahertz pulse is essential for interpreting the results: spectroscopy measurements on polystyrene foam and terahertz images of a plastic coin. Both measurements show a sample-induced rotation of the terahertz electric field vector, which is surprisingly large and is a strong function of frequency. A promising aspect of our setup is the possibility of simultaneously measuring both transversal electric field components.