How can I measure the current drawn by a soil hygrometer?
The best way to know what the current draw can be is to consult the datasheet.  If that is not available, and this is for production, go get something that does have a datasheet.

You can also just measure the current.  However, keep in mind that only tells you what that unit draws on that day at that temperature.

However, looking at the bigger picture, what's the point of embedding someone else's unit into yours?  The circuit for a moisture meter is very simple, and is probably easier to incorporate into your own product than to try to embed someone else's.  Also, there are a lot of bad ways to try to measure resistance between electrodes.  Something that doesn't come with a datasheet doesn't inspire confidence that someone that actually knew what they were doing designed the unit.  Since it appears to be just a simple analog circuit, it is quite unlikely to be using a good technique.

The best method pretty much requires a microcontroller doing a 4-phase measurement.  I discuss it in the context of detecting water, but the principle is the same.  See https://electronics.stackexchange.com/a/33938/4512, https://electronics.stackexchange.com/a/103330/4512, and https://electronics.stackexchange.com/a/28485/4512.