  We present a search for the baryon number $B$ and lepton number $L$ violating
decays $\tau^- \rightarrow \Lambda \pi^-$ and $\tau^- \rightarrow \bar{\Lambda}
\pi^-$ produced from the $e^+e^-\to \tau^+\tau^-$ process, using a 364
fb$^{-1}$ data sample collected by the Belle~II experiment at the SuperKEKB
collider. No evidence of signal is found in either decay mode, which have
$|\Delta(B-L)|$ equal to $2$ and $0$, respectively. Upper limits at 90\%
credibility level on the branching fractions of $\tau^- \rightarrow
\Lambda\pi^-$ and $\tau^- \rightarrow \bar{\Lambda}\pi^-$ are determined to be
$4.7 \times 10^{-8}$ and $4.3 \times 10^{-8}$, respectively.
