We examine the relationship between the strength of the intensity fluctuations and the polarimetric properties of a random electromagnetic field composed of a Gaussian, random field, and nonrandom field, and we present a method for determining the state of polarization of the Gaussian random field. The approach relies on incoherently mixing a Gaussian random field with a controllable reference field and measuring the intensity fluctuations of their superposition. We demonstrate that by controlling the reference field, the full polarimetric information about the Gaussian random field can be uniquely determined.