  We present results of radiative transfer calculations to measure the impact
of gas bulk rotation on the morphology of the Lyman $\alpha$ emission line in
distant galaxies. We model a galaxy as a sphere with an homogeneous mixture of
dust and hydrogen at a constant temperature. These spheres undergo solid-body
rotation with maximum velocities in the range 0-300 \kms and neutral hydrogen
optical depths in the range $\tau_{\rm H}=10^{5}-10^{7}$. We consider two types
of source distributions in the sphere: central and homogeneous. Our main result
is that rotation introduces a dependence of the line morphology with viewing
angle and rotational velocity. Observations with a line of sight parallel to
the rotation axis yield line morphologies similar to the static case. For lines
of sight perpendicular to the rotation axis both the intensity at the line
center and the line width increase with rotational velocity. Along the same
line of sight, the line becomes single peaked at rotational velocities close to
half the line width in the static case. Notably, we find that rotation does not
induce any spatial anisotropy in the integrated line flux, the escape fraction
or the average number of scatterings. This is because Lyman {\alpha} scattering
through a rotating solid-body proceeds identical as in the static case. The
only difference is the doppler shift from the different regions in the sphere
that move with respect to the observer. This allows us to derive an analytic
approximation for the viewing-angle dependence of the emerging spectrum, as a
function of rotational velocity.
