  We consider massive half-integer higher spin fields coupled to an external
constant electromagnetic field in flat space of an arbitrary dimension and
construct a gauge invariant Lagrangian in the linear approximation in the
external field. A procedure for finding the gauge-invariant Lagrangians is
based on the BRST construction where no off-shell constraints on the fields and
on the gauge parameters are imposed from the very beginning. As an example of
the general procedure, we derive a gauge invariant Lagrangian for a massive
fermionic field with spin 3/2 which contains a set of auxiliary fields and
gauge symmetries.
