Can this croton clipping be propagated in water?

I don;t really know. I think the most reliable ways are to air layer, or just treat with rooting hormone and stick in a pot of soil (which is how I root all mine. In SUMMER. Outside. When its hot, humid and there is a lot of full sun).
@ScotTi would know

@gina1960 is correct. I take clippings about 6-8 inches long with one or two leaves. Brush it with the rooting hormone and plant in a light potting soil.

If it's warm enough outside put them in bright dappled but no direct sun. If you keep them on a flat you can move them easily.

If it is too cold in your location you might invest in a heating mat and a grow light.

Gina and Tom have given great advice.
My choice for rooting Crotons is the air layering method using sphagnum moss. This allows for a larger (12"+) rooted starter plant.
If you prefer to go with water rooting wait until late spring. Use a 3 "- 5" cutting and keep the water warm.