  We introduce a two-dimensional (2D) discrete nonlinear Schr\"{o}dinger (DNLS)
equation with self-attractive cubic nonlinearity in a rotating reference frame.
The model applies to a Bose-Einstein condensate stirred by a rotating strong
optical lattice, or light propagation in a twisted bundle of nonlinear fibers.
Two species of localized states are constructed: off-axis fundamental solitons
(FSs), placed at distance $R$ from the rotation pivot, and on-axis (R=0) vortex
solitons (VSs), with vorticities $% S=1$ and 2. At a fixed value of rotation
frequency $\Omega $, a stability interval for the FSs is found in terms of the
lattice coupling constant $C$, $% 0<C<C_{\mathrm{cr}}(R)$, with monotonically
decreasing $C_{\mathrm{cr}}(R)$. VSs with S=1 have a stability interval,
$\tilde{C}_{\mathrm{cr}%}^{(S=1)}(\Omega)<C<C_{\mathrm{cr}}^{(S=1)}(\Omega)$,
which exists for $% \Omega $ below a certain critical value,
$\Omega_{\mathrm{cr}}^{(S=1)}$. This implies that the VSs with S=1 are
\emph{destabilized} in the weak-coupling limit by the rotation. On the
contrary, VSs with S=2, that are known to be unstable in the standard DNLS
equation, with $\Omega =0$, are \emph{stabilized} by the rotation in region
$0<C<C_{\mathrm{cr}}^{(S=2)}$%, with $C_{\mathrm{cr}}^{(S=2)}$ growing as a
function of $\Omega $. Quadrupole and octupole on-axis solitons are considered
too, their stability regions being weakly affected by $\Omega \neq 0$.
