It is but you need both a big hunk of mass and a way to detect the neutrino interactions inside it. Ice Cube is shot through with detectors. One of the OG detectors measured the particular isotope created during interactions.

https://en.wikipedia.org/wiki/Homestake_experiment#Methodolo...

The Super-Kamiokande has photomultipliers staring at a bunch of water looking for Cherenkov radiation resulting from neutrino interactions

https://en.wikipedia.org/wiki/Super-Kamiokande

None of these are much of a practical option with the moon.