  We show that for a Baire generic rotation number $\alpha \in \mathbb{R} /
\mathbb{Z}$, the set of area preserving $C^\infty$-pseudo-rotations of the
annulus $\mathbb{A}$ with rotation number $\alpha$ equals the closure of the
set of area preserving $C^\infty$-pseudo-rotations which are smoothly conjugate
to the rotation $R_{\alpha}$. As a corollary, a $C^\infty$-generic area
preserving pseudo-rotation of the annulus with a Baire generic rotation number
$\alpha$ is weakly mixing.
