  We present a detailed study of quantum oscillations in the
antiferromagnetically ordered pnictide compound SrFe$_2$As$_2$ as the angle
between the applied magnetic field and crystalline axes is varied. Our
measurements were performed on high quality single crystals in a
superconducting magnet, and in pulsed magnetic fields up to 60 T, allowing us
to observe orbits from several small Fermi surface pockets. We extract the
cyclotron effective mass $m^{\star}$ and frequency $F$ for these orbits and
track their values as the field is rotated away from the c-axis. While a
constant ratio of $m^{\star}/F$ is observed for one orbit as expected for a
parabolic band, a clear deviation is observed for another. We conclude that
this deviation points to an orbit derived from a band with Dirac dispersion
near the Fermi level.
