  Chiral superconductors spontaneously break time-reversal symmetry and host
topologically protected edge modes, supposedly generating chiral edge currents
which are typically taken as a characteristic fingerprint of chiral
superconductivity. However, recent studies have shown that the total edge
current in two dimensions (2D) often vanishes for all chiral superconductors
except for chiral $p$-wave, especially at low temperatures, thus severely
impeding potential experimental verification and characterization of these
superconductors. In this work, we use quasiclassical theory of
superconductivity to study mesoscopic disc-schaped chiral $d$-wave
superconductors. We find that mesoscopic finite-size effects cause a dramatic
enhancement of the total charge current and orbital magnetic moment (OMM), even
at low temperatures. We study how these quantities scale with temperature,
spontaneous Meissner screening, and system radius $\mathcal{R} \in
[5,200]\xi_0$ with superconducting coherence length $\xi_0$. We find a general
$1/\mathcal{R}$ scaling in the total charge current and OMM for sufficiently
large systems, but this breaks down in small systems, instead producing a local
maximum at $\mathcal{R} \approx 10{\text{--}}20\xi_0$ due to mesoscopic
finite-size effects. These effects also cause a spontaneous charge-current
reversal opposite to the chirality below $\mathcal{R} < 10\xi_0$. Our work
highlights mesoscopic systems as a route to experimentally verify chiral
$d$-wave superconductivity, measurable with magnetometry.
