This is a lengthy thread on the subject of getting citizenship (the thread begins in 2004 and ends in 2016):
If you want to become a citizen of Taiwan, the following may offer information that will be helpful to you:
RESIDENCE:
Many foreigners in Taiwan have residence in the form of an Alien Residence Card. This green colored card allows you to legally stay in Taiwan based on the fact that you have a legal job (employer is indicated on the card) or that you are married to a local.
CITIZENSHIP:
To be a citizen of Taiwan means that you have an actual ROC ID card. With this, you can get phone number…
I’m posting a link of the same thread, from the old board (bearing in mind that I’m not sure that the link will always work):
According to Wikipedia, an American named Lin Dao-ming, also called T. C. Lin, became a citizen first, in 1994, and was then drafted into the army in 1995:
Taiwan imposes conscription on all qualified males of military age, including naturalized citizens. Friends of the former Locke — now Lin — did not expect he would be called up, since he was of foreign origin, but his draft notice indeed arrived in late 1995. His military service coincided with a tense time for Taiwan, as the Third Taiwan Strait Crisis unfolded in early 1996.
Like most young men in Taiwan, Lin was not looking forward to military service, but he found to his surprise that it was ...
Lin discusses some of his army experience here:
http://www.romanization.com/books/poagao/chap02.html
This looks like another account, written in 2011, by someone else who was inducted into the army:
For voluntary service, this seems to be a translation of the pertinent law (thanks to @tempogain and @tando ):
https://law.mnd.gov.tw/FLAWDAT0202.asp?lsid=FL005463
I got that link from this thread, which is also contained in @WindyTown ’s Google results:
I am a US citizen and i am planning on moving to Taiwan, i am currently learning traditional Chinese and will be doing a year long language course when i arrive in Taiwan. I would like to know if it is possible to join the ROC military as a foreigner.
I hope this helps, or at least does no harm.