  We investigate the Noether symmetries of the Lagrangian for the stationary
rotating BTZ-type three-dimensional spacetimes in $f(R)$ theory of gravity. A
detailed analysis of Noether symmetries of (2+1)-dimensional rotating BTZ-type
black hole spacetime model is presented. Applying the Noether symmetry
approach, the first integrals (constants of motion) for each of Noether
symmetries are obtained to look for the exact solutions. After solving the
first integral equations depending on the form of the function $f(R)$, we
derived some new (2+1)-dimensional rotating BTZ-type black hole solutions. We
discussed the physical implications of the derived exact solutions. The
thermodynamical properties of the obtained BTZ-type black hole solutions are
analyzed by making use of the mass $M$ and the angular momentum $J$ in terms of
$r_{\pm}$, where $r_+$ is the event horizon and $r_{-}$ is the inner horizon.
Further, it is shown that thermodynamic quantities obey the first law, and the
Smarr-like formulas of the solutions we found are obtained.
