  We study the gravitational field of a spinning radiation beam-pulse in a
higher dimensional spacetime. We derive first the stress-energy tensor for such
a beam in a flat spacetime and find the gravitational field generated by it in
the linear approximation. We demonstrate that this gravitational field can also
be obtained by boosting the Lense-Thirring metric in the limit when the
velocity of the boosted source is close to the velocity of light. We then find
an exact solution of the Einstein equations describing the gravitational field
of a polarized radiation beam-pulse in a space-time with arbitrary number of
dimensions. In a $D-$dimensional spacetime this solution contains $[D/2]$
arbitrary functions of one variable (retarded time $u$), where $[d]$ is the
integer part of $d$. For the special case of a 4-dimensional spacetime we study
effects produced by such a relativistic spinning beam on the motion of test
particles and light.
