I installed ibus-anthy but it didn't appear on keyboard layout.
I have the same problem before with iBus. It works on Ubuntu Unity desktop, but not in elementaryOS. I've not yet try it again. I use NIMF instead to type in Japanese or Korean.
If you like to install NIMF for Japanese or Korean you can install with command below :
sudo apt install nimf anthy* libanthy* libhangul*
Then on your terminal :
then select NIMF as default IME, click OK. Logout then Login again from your account or restart, whatever you like. It will appear on the corner (left side of SystemKeyboard) select the IME that you want.