  In this article we prove a reducibility result for the linear Schr\"odinger
equation on the sphere $\mathbb{S}^{n}$ with quasi-periodic in time
perturbation. Our result includes the case of unbounded perturbation that we
assume to be of order strictly less than 1/2 and satisfying some parity
condition. As far as we know, this is one of the few reducibility results for
an equation in more than one dimension with unbounded perturbations. We notice
that our result does not requires the use of the pseudo-differential calculus.
