  A non-minimal coupling for spin $3/2$ fields is obtained. We use the fact
that the Rarita-Schwinger field equations are the square root of the full
linearized Einstein field equations in order to investigate the form of the
interaction for the spin $3/2$ field with gauge fields. We deduce the form of
the interaction terms for the electromagnetic and non-Abelian Yang-Mills fields
by implementing appropiate energy momentum tensors on the linearized Einstein
field equations. The interaction found for the electromagnetic case happens to
coincide with the dipole term found by Ferrara {\it et al} by a very different
procedure, namely by demanding $g=2$ at the tree level for the electromagnetic
interaction of arbitrary spin particles. The same interaction is found by using
the resource of linearized Supergravity N=2. For the case of the Yang-Mills
field Supergravity N=4 is linearized, providing the already foreseen
interaction.
