  Sr$_{2}$RuO$_{4}$ is one of the most promising candidates of a topological
superconductor with broken time-reversal symmetry, because a number of
experiments have revealed evidences for a spin-triplet chiral $p$-wave
superconductivity. In order to clarify the time-reversal symmetry of
Sr$_{2}$RuO$_{4}$, we introduce a novel test that examines the invariance of
the Josephson critical current under the inversion of both the current and
magnetic fields, in contrast to the detection of a spontaneous magnetic field
employed in past experiments. Analyses of the transport properties of the
planar and corner Josephson junctions formed between Sr$_{2}$RuO$_{4}$ and Nb
reveal the time-reversal invariant superconductivity, most probably helical
$p$-wave, of Sr$_{2}$RuO$_{4}$. This state corresponds to a yet-to-be confirmed
$topological crystalline superconductivity$ that can host two Majorana edge
modes at the surface protected by crystalline mirror symmetry.
