Turbulent flows appear in many geophysical systems of climatic interest and are characterized by an enormous number of degrees of freedom. In the past, many claims have been made regarding the existence of a low dimensional description of their dynamics without convincing evidence. Here, we provide the first experimental evidence of the existence of a random attractor in a fully turbulent flow. The reconstruction of the attractor is made via classical embedding of a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow. By increasing the asymmetry, a phase transition occurs. The stochastic Duffing equations can reproduce most of the quantitative properties of the experimental attractor, namely the number of fixed points and the Lyapunov exponents. Our findings open the way to solve a long standing controversy in geophysics, about the existence of an attractor in the atmospheric or climate dynamics. Indeed many problems of geophysical fluid dynamics featuring the existence of multiple stationary states such as positive and negatives El Nino states or the appearance of blocking phases of mid-latitude circulation dynamics may be described by low-dimensional stochastic attractors provided the choice of a suitable parameter reflecting the system symmetries.