We study celestial amplitudes in (super) Yang-Mills theory using a parametrization of the spinor helicity variables where their overall phase is not fixed by the little group action. In this approach the spin constraint $h-\overline{h}=J$ for celestial conformal primaries emerges naturally from a new Mellin transform, and the action of conformal transformations on celestial amplitudes is derived. Applying this approach to $N=4$ super Yang-Mills, we show how the appropriate definition of on-shell superspace coordinates leads naturally to a formulation of chiral celestial superamplitudes and a representation of the generators of the four-dimensional superconformal algebra on the celestial sphere, which by construction annihilate all tree-level celestial superamplitudes.