If you or your spouse read Chinese,
配偶為外國國籍之大陸地區人民申請赴台隨行團聚送件須知
I don’t know whether the above document is still valid or outdated, though, according to it, she needs to wait in the PRC, until you get your ARC in Taiwan.
Added
I found it was posted on the site of TECO in Japan on Mar 14 in 2016. So, I think it may be still valid.
https://www.roc-taiwan.org/jp/post/427.html
is it really allowed?