Semiconductor Bi$_2$O$_2$Se nanolayers of high crystal quality have been realized via epitaxial growth. These two-dimensional (2D) materials possess excellent electron transport properties with potential application in nanoelectronics. It is also strongly expected that the 2D Bi$_2$O$_2$Se nanolayers could be of an excellent material platform for developing spintronic and topological quantum devices, if the presence of strong spin-orbit interaction in the 2D materials can be experimentally demonstrated. Here, we report on experimental determination of the strength of spin-orbit interaction in Bi$_2$O$_2$Se nanoplates through magnetotransport measurements. The nanoplates are epitaxially grown by chemical vapor deposition and the magnetotransport measurements are performed at low temperatures. The measured magnetoconductance exhibits a crossover behavior from weak antilocalization to weak localization at low magnetic fields with increasing temperature or decreasing back gate voltage. We have analyzed this transition behavior of the magnetoconductance based on an interference theory which describes the quantum correction to the magnetoconductance of a 2D system in the presence of spin-orbit interaction. Dephasing length and spin relaxation length are extracted from the magnetoconductance measurements. Comparing to other semiconductor nanostructures, the extracted relatively short spin relaxation length of ~150 nm indicates the existence of strong spin-orbit interaction in Bi$_2$O$_2$Se nanolayers.
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