  Based on $4.4~\text{fb}^{-1}$ of $e^{+}e^{-}$ annihilation data collected at
the center-of-mass energies between $4.60$ and $4.70~\text{GeV}$ with the
BESIII detector at the BEPCII collider, the pure \textit{W}-boson-exchange
decay $\Lambda_{c}^{+}\to\Xi^{0}K^{+}$ is studied with a full angular analysis.
The corresponding decay asymmetry is measured for the first time to be
$\alpha_{\Xi^{0}K^{+}}=0.01\pm0.16({\rm stat.})\pm0.03({\rm syst.})$. This
result reflects the non-interference effect between the $S$- and $P$-wave
amplitudes. The phase shift between $S$- and $P$-wave amplitudes has two
solutions, which are $\delta_{p}-\delta_{s}=-1.55\pm0.25({\rm
stat.})\pm0.05({\rm syst.})~\text{rad}$ or $1.59\pm0.25({\rm
stat.})\pm0.05({\rm syst.})~\text{rad}$.
