The Rees-Sciama effect produced in mergers of galaxy clusters is discussed, and an analytical approximation to compute this effect from numerical simulations is given. Using this approximation and a novel model describing the physics of the merger, we characterize the spatial properties and symmetries of the Rees-Sciama signal. Based on these properties, we propose a method to extract the physical parameters of the merger, which relies on the computation of the quadrupole moment of the observed brightness distribution on the sky. The relationships between the quadrupole coefficients and the physical parameters of the merger (physical separation, projection angle on the sky and angular momentum) are discussed. Finally, we propose a method to co-add coherently the RS signals from a sample of cluster mergers, to achieve a statistical detection of the effect for those cases where individual signals are masked by the kinetic SZ effect, the primordial CMB components, and by observational noise.