  Strong spin-orbital-coupling magnetic systems with the honeycomb structure
can provide bond-directional interactions which may result in Kitaev quantum
spin liquids and exotic anyonic excitations. However, one of the key
ingredients in real materials$-$disorders$-$has been much less studied in
Kitaev systems. Here we synthesized a trigonal SrIr$_2$O$_{6-\delta}$ with
$\delta \approx 0.25$, which consists of two-dimensional honeycomb Ir planes
with edge-sharing IrO$_6$ octahedra. First-principles computation and
experimental measurements suggest that the electronic system is gapped, and
there should be no magnetic moment as the Ir$^{5+}$ ion has no unpaired
electrons. However, significant magnetism has been observed in the material,
and it can be attributed to disorders that are most likely from oxygen
vacancies. No magnetic order is found down to 0.05 K, and the low-temperature
magnetic properties exhibit power-law behaviors in magnetic susceptibility and
zero-field specific heat, and a single-parameter scaling of the specific heat
under magnetic fields. These results provide strong evidence for the existence
of the random singlet phase in SrIr$_2$O$_{6-\delta}$, which offers a different
member to the family of spin-orbital entangled iridates and Kitaev materials.
