  We prove that the critical surface quasi-geostrophic equation driven by a
force $f$ possesses a compact global attractor in $L^2(\mathbb T^2)$ provided
$f\in L^p(\mathbb T^2)$ for some $p>2$. First, the De Giorgi method is used to
obtain uniform $L^\infty$ estimates on viscosity solutions. Even though this
does not provide a compact absorbing set, the existence of a compact global
attractor follows from the continuity of solutions, which is obtained by
estimating the energy flux using the Littlewood-Paley decomposition.
