Isolated multi-MeV $\gamma$ -rays with attosecond duration, high collimation and beam angular momentum (BAM) may find many interesting applications in nuclear physics, astrophysics, etc. Here, we propose a scheme to generate such $\gamma$ -rays via nonlinear Thomson scattering of a rotating relativistic electron sheet driven by a few-cycle twisted laser pulse interacting with a micro-droplet target. Our model clarifies the laser intensity threshold and carrier-envelope phase effect on the generation of the isolated electron sheet. Three-dimensional numerical simulations demonstrate the $\gamma$ -ray emission with 320 attoseconds duration and peak brilliance of $9.3\times 10^{24}$ photons s ${}^{-1}$ mrad ${}^{-2}$ mm ${}^{-2}$ per 0.1 $\%$ bandwidth at 4.3 MeV. The $\gamma$ -ray beam carries a large BAM of $2.8 \times 10^{16}\mathrm{\hslash}$ , which arises from the efficient BAM transfer from the rotating electron sheet, subsequently leading to a unique angular distribution. This work should promote the experimental investigation of nonlinear Thomson scattering of rotating electron sheets in large laser facilities.