  Ballistic transport through an impurity-free section of the Corbino disk in
graphene is investigated by means of the Landauer-B\"{u}ttiker formalism in the
mesoscopic limit. In the linear-responce regime the conductance is quantized in
steps close to integer multiples of $4e^{2}/h$, yet Fabry-Perot oscillations
are strongly suppressed. The quantization arises for small opening angles
$\theta\lesssim\pi/3$ and large radii ratios $R_2/R_1\gtrsim{}10$. We find that
the condition for emergence of the $n$-th conductance step can be written as
$\sqrt{n}\theta/\pi\ll{}1$. A brief comparison with the conductance spectra of
graphene nanoribbons with parallel edges is also provided.
