Using quantum arguments, Witten proposed that a magnetic monopole acquires electric charge in a theta vacuum. In a formulation where the theta vacua of a gauge theory are described by the vacua of a massless Chern-Simons 3-form, we showed that the Witten effect can already be captured at the level of effective classical equations of motion. Beyond this, we numerically demonstrated that a magnetic monopole exhibits polarizability when placed in a constant background electric field. In this talk, I will give a brief introduction to the 3-form formulation of theta vacua and present our numerical results on both the Witten effect and the polarizability of magnetic monopoles.