  Motivated by recent proposals in hep-th/0202021 and hep-th/0204051 we develop
semiclassical quantization of superstring in $AdS_5 x S^5$. We start with a
classical solution describing string rotating in $AdS_5$ and boosted along
large circle of $S^5$. The energy of the classical solution $E$ is a function
of the spin $S$ and the momentum $J$ (R-charge) which interpolates between the
limiting cases S=0 and J=0 considered previously. We derive the corresponding
quadratic fluctuation action for bosonic and fermionic fields from the GS
string action and compute the string 1-loop (large $\lambda= {R^4\over \a'^2}$)
correction to the classical energy spectrum in the $(S,J)$ sector. We find that
the 1-loop correction to the ground-state energy does not cancel for non-zero
$S$. For large $S$ it scales as $\ln S$, i.e. as the classical term, with no
higher powers of $\ln S$ appearing. This supports the conjecture made in
hep-th/0204051 that the classical $E-S = a \ln S$ scaling can be interpolated
to weak coupling to reproduce the corresponding operator anomalous dimension
behaviour in gauge theory.
