We present a detailed study of the magnetic anisotropy of RuCl₃ – a layered honeycomb structure of effective spin-1/2 moments. The strong spin-orbit coupling of ruthenium enhances magnetic frustration, which leads to a zigzag antiferromagnetic (AFM) ground state at 7K – a temperature much lower than the exchange interaction energy scale. With magnetic fields of roughly 10 T, AFM order is suppressed and an unconventional spin state emerges. This state, characterized by an unsaturated magnetization, persists up to magnetic fields of order 100 T. We use a newly-developed technique – resonant torsion magnetometry – to explore the temperature evolution of the magnetic anisotropy in the high-field state of RuCl₃. The high sensitivity of this technique allows us to measure a single crystallographic, and hence magnetic, domain. With increasing magnetic field, we observe a single transition associated with the suppression of AFM order. Above this transition, the magnetic anisotropy saturates (unlike the isotropic component of the magnetization), with a saturation field that scales linearly with temperature. Our data shows that the energy scale that determines the magnetic anisotropy is set only by field and temperature. This suggests that the intrinsic energy scale is driven to zero by strong correlations – a signature of a fluid-like spin state that is decoupled from the underlying exchange interactions.