"A 5,000-year-old stone structure in the shape of the crescent moon in northern Israel has been identified to be an ancient monument, predating much of the construction of Stonehenge in England and Great Pyramid of Giza in Egypt." Source: The Telegraph.
Notes: Known as Rujum en-Nabi Shua'ayb or Jethro Cairn, this stone structure was originally thought to have been part of a city's defensive walls when it was discovered near the Sea of Galilee earlier this century, but a student working on his master's degree has suggested that the structure is actually a very ancient monument.
Jethro Cairn dates back to the early Bronze Age (3000 BC?), which would make it one of the oldest, if not the oldest, stone monuments discovered so far, assuming that the dating is accurate and that it really is a monument. As far as I can tell, the idea that this is a "Moon God" monument is based strictly on its sickle or crescent-moon shape and it's been suggested that it was dedicated to the moon god Sin:
"One of the most important gods in Mesopotamian mythology, Sin, also known as ‘Nanna’, is symbolised as a crescent moon and is often depicted riding on a winged bull," according to the Encyclopedia Britannica.
So far, this interpretation of the site is just that -- an interpretation -- but "other large rock structures" such as cairns and circles have been found near the site, according to Live Science.