Glasses, amorphous solid phases nearly always out of equilibrium, remain poorly understood despite recent progress. Here we show by quantitative real-space experiments and computer simulations the existence of an equilibrium glass-forming phase which forms due to a subtle interplay between the rotational and translational degrees of freedom in a system of charged colloidal rods. In this rotational glass-forming phase, the positional coordinates are glass-like, while the rotations remain liquid-like. This phase can be reversibly switched into a crystalline solid through a first-order phase transition with minimal particle rearrangements by an external electric field. We speculate that this rotator glass-like phase forms due to the anisotropic particle interactions at higher volume fractions, destabilizing the crystal. Finding an equilibrium glassy rotator phase will lead to new insights on how translations and rotations affect phase behavior, including glass formation and, additionally, allow new theoretical approaches to be used to study the glass transition.