  We examine the distribution of the magnetic anisotropy (MA) experienced by a
magnetic impurity embedded in a metallic nano-grain. As an example of a generic
magnetic impurity with partially filled $d$-shell, we study the case of $d^{1}$
impurities imbedded into ordered and disordered Au nano-grains, described in
terms of a realistic band structure. Confinement of the electrons induces a
magnetic anisotropy that is large, and can be characterized by 5 real
parameters, coupling to the quadrupolar moments of the spin. In ordered
(spherical) nano-grains, these parameters exhibit symmetrical structures and
reflect the symmetry of the underlying lattice, while for disordered grains
they are randomly distributed and, - for stronger disorder, - their
distribution is found to be characterized by random matrix theory. As a result,
the probability of having small magnetic anisotropies $K_L$ is suppressed below
a characteristic scale $\Delta_E$, which we predict to scale with the number of
atoms $N$ as $\Delta_E\sim 1/N^{3/2}$. This gives rise to anomalies in the
specific heat and the susceptibility at temperatures $T\sim \Delta_E$ and
produces distinct structures in the magnetic excitation spectrum of the
clusters, that should be possible to detect experimentally.
