Try using pamac if you don’t have pacman:
pamac install manjaro-asian-input-support-fcitx
After installing it, you should have fcitx enabled for Asian characters input.
Sorry, this post should have replied @Canartikin 
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有点好奇，什么情况下预装的manjaro会没有pacman？
By the way, what’s inside that package? I have fcitx working just fine on my desktop (besides of Telegram and I was wondering what exactly is the difference of that package from fcitx+fcitx-rime (in my case)
之前好像有陣子 Manjaro 團隊想用 pamac 來取代原先的 pacman 所以在 ISO 中移除了 pacman，現在應該是兩者同時預裝了？
That package is a wrapper of fcitx and some necessary environmental variable configurations. Basically, you need to set up some environmental variables to make fcitx work after installation. With this package, it can save you some hassles.
Here’re the steps to set up fcitx if you would like to do it the hard way:
https://wiki.archlinux.org/index.php/Fcitx
In you case, fcitx is the framework, and fcitx-rime is the actual input method that you use.