  We compute the frequency-dependent shear and bulk viscosity spectral
functions of an interacting Fermi gas in a quantum virial expansion up to
second quadratic order in the fugacity parameter $z=e^{\beta \mu}$, which is
small at high temperatures. Calculations are carried out using a diagrammatic
finite-temperature field-theoretic framework, in which the analytic
continuation from Matsubara to real frequencies is carried out in closed
analytic form. Besides a possible zero-frequency Drude peak, our results for
the spectral functions show a broad continuous spectrum at all frequencies with
an additional bound-state contribution for frequencies larger than the
dimer-breaking energy. Our results are consistent with various sum rules and
universal high-frequency tails. In the low-frequency limit, the shear viscosity
spectral function is recast as a collision integral, which reproduces known
results for the static shear viscosity from kinetic theory. Our findings for
the static bulk viscosity of a Fermi gas near unitarity, however, show a
nonanalytic dependence on the scattering length, at variance with kinetic
theory.
