A homeomorphism of the annulus without any periodic point is called a pseudo-rotation. Each pseudo-rotation has a unique rotation number in $\mathbb{R} / \mathbb{Z}$. 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 to 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 is weakly mixing. This is a joint work with Barney Bramham.