  For $0 \leq s \leq 1$ and $0 \leq t \leq 3$, a set $F \subset \mathbb{R}^{2}$
is called a circular $(s,t)$-Furstenberg set if there exists a family of
circles $\mathcal{S}$ of Hausdorff dimension $\dim_{\mathrm{H}} \mathcal{S}
\geq t$ such that $$\dim_{\mathrm{H}} (F \cap S) \geq s, \qquad S \in
\mathcal{S}.$$ We prove that if $0 \leq t \leq s \leq 1$, then every circular
$(s,t)$-Furstenberg set $F \subset \mathbb{R}^{2}$ has Hausdorff dimension
$\dim_{\mathrm{H}} F \geq s + t$. The case $s = 1$ follows from earlier work of
Wolff on circular Kakeya sets.
