  A large portion of the studies concerning the quasinormal mode frequencies of
a Kerr black hole have focused only on achieving higher numerical accuracy with
limited emphasis on providing their physical interpretation. In this article,
we partially address this issue by computing the quasinormal mode frequency
spectrum of a Kerr black hole using the theory of Regge poles. By considering
the retarded Green's function of the Teukolsky equation, we establish for
scalar, electromagnetic and gravitational perturbations an equation linking the
Regge poles to the quasinormal frequencies and we solve it in the
high-frequency regime to get "semiclassical" relations permitting us to obtain
the complex frequencies of the weakly damped quasinormal modes from the Regge
trajectories. Numerical results concerning gravitational perturbations ($s=-2$)
are displayed. They are in excellent agreement with the "exact" ones in the
eikonal regime $(\ell \gg 1)$ and in very good agreement even for lower values
of $\ell$. Moreover, the splitting of each Regge pole of the Schwarzschild
black hole into an infinite number of Kerr Regge poles explains the breaking of
the azimuthal degeneracy of the quasinormal frequencies of the Schwarzschild
black hole due to rotation. Our work is a first step to extend to Kerr black
holes the approach developed for static spherically symmetric black holes which
allowed, from a geometrical interpretation of the Regge poles in terms of the
properties of the unstable circular null geodesics lying on the photon sphere,
to derive accurate analytical formulas for the Regge trajectories and, as a
by-product, for the complex frequencies of the weakly damped quasinormal modes.
