Slings are known to have been used commonly everywhere from the near east to the new world. I have never seen them mentioned in east Asia though. Were they just very uncommon, or did the east Asians just never use slings?
Used in Tibet and Mongolia into recent times, used in Medieval Japan, Three Kingdoms Korea.
A couple of Japanese examples:
https://edb.kulib.kyoto-u.ac.jp/exhibit/b35/image/09/b35l0150.html
https://edb.kulib.kyoto-u.ac.jp/exhibit/b35/image/09/b35s0151.html
These are AFAIK depictions of a ritual battle (i.e., a mock battle for ceremonial/ritual purposes). But they were used in real battles too. See, e.g., http://slinging.org/forum/YaBB.pl?num=1425951864
According to Robert E. Dohrenwend, "The Sling: Forgotten Firepower of Antiquity", Journal of Asian Martial Arts, Vol. 11 No. 2, 28-49 (2002), it was also used in China in recent times. I haven't seen any primary sources or archeological evidence for Chinese use, but it's certainly plausible, given that all of China's neighbours, N, E, S, and W, used the sling.
They weren't common as a military weapon in East Asia - the crossbow, bow, and (for almost a thousand years in China) the gun dominated. But it was certainly carried and used by herders.