  Large scale features of a randomly isotropically forced incompressible and
unbounded rotating fluid are examined in perturbation theory. At first order in
both the random force amplitude and the angular velocity we find two types of
modifications to the fluid equation of motion. The first correction transforms
the molecular shear viscosity into a (rotation independent) effective
viscosity. The second perturbative correction leads to a new large scale
non-dissipative force proportional to the fluid angular velocity in the slow
rotation regime. This effective force does no net work and alters the
dispersion relation of inertial waves propagating in the fluid. Both
dynamically generated corrections can be identified with certain components of
the most general axisymmetric ``viscosity tensor'' for a Newtonian fluid.
