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We prove that the critical surface quasi-geostrophic equation driven by aforce $f$ 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 toobtain uniform $L^\infty$ estimates on viscosity solutions. Even though thisdoes not provide a compact absorbing set, the existence of a compact globalattractor follows from the continuity of solutions, which is obtained byestimating the energy flux using the Littlewood-Paley decomposition.

The existence of a global attractor for the forced critical surface quasi-geostrophic equation in $L^2$