The modern Japanese word for "scarecrow" is kakashi. I had never thought much about what the etymology was until I found it in the Vocabularia in a slightly different form:

Cagaxi. Eſpantalho das ſementeiras per a eſpãtar os porcos do mato, ou veados.
Kagashi. Scarecrow of the sowing [?] to scare boars, or deer.

So the second /k/ was originally voiced. The current consensus (e.g. Maeda 300-301, Sugimoto 185) seems to be that the word shares a root with modern kagu "smell" and literally means something like "causer of the act of smelling", and that the original kagashi was not a human figure but a hunk of burnt game or clump of scorched hair tied to a stake, which quite understandably kept the animals away.

The usual way of spelling kakashi is 案山子, which is obviously not etymologically related to the word itself. Instead, 案山子 is a Chinese word, apparently imported in the Zen literature. It seems that 案山 referred to a relatively flat and accessible part of a mountain, where one might have a field for growing things, and 子 was added with its common meaning of "-thing", "-guy", etc.

Everyone seems to quote the same passage from the Transmission of the Lamp 景德傳燈錄 in support of this:

僧曰。不会。師曰。面前案山子也不会。

I'm a little leery of translating this without context, but it looks like it says:

The monk said, "I don't understand." The master said, "The scarecrow out front [or: in front of you?] doesn't understand either."

Works cited

• Maeda Tomiyoshi 前田富棋, ed.Nihongogen daijiten. Tokyo: Shōgakukan, 2005.
• Sugimoto, Tsutomu 杉本つとむ. Gogenkai. Tokyo: Tōkyō Shoseki, 2005.
• Vocabulario da Lingoa de Iapam. Nagasaki, 1603. Tokyo: Benseisha 勉誠社, 1978.