  We report on the observation of superconductivity in LaRh$_2$As$_2$, which is
the analogue without $f$-electrons of the heavy-fermion system with two
superconducting phases CeRh$_2$As$_2$. A zero-resistivity transition, a
specific-heat jump and a drop in magnetic ac susceptibility consistently point
to a superconducting transition at a transition temperature of $T_c = 0.28$\,K.
The magnetic field-temperature superconducting phase diagrams determined from
field-dependent ac-susceptibility measurements reveal small upper critical
fields $\mu_{\mathrm{0}}H_{c2} \approx 12$\,mT for $H\parallel ab$ and
$\mu_{\mathrm{0}}H_{c2} \approx 9$\,mT for $H\parallel c$. The observed
$H_{c2}$ is larger than the estimated thermodynamic critical field $H_c$
derived from the heat-capacity data, suggesting that LaRh$_2$A$s_2$ is a
type-II superconductor with Ginzburg-Landau parameters $\kappa^{ab}_{GL}
\approx 1.9$ and $\kappa^{c}_{GL}\approx 2.7$. The microscopic Eliashberg
theory indicates superconductivity to be in the weak-coupling regime with an
electron-phonon coupling constant $\lambda_{e-ph} \approx 0.4$. Despite a
similar $T_c$ and the same crystal structure as the Ce compound, LaRh$_2$As$_2$
displays conventional superconductivity, corroborating the substantial role of
the 4$f$ electrons for the extraordinary superconducting state in
CeRh$_2$As$_2$.
