Anthy is an IBUS method to input Japanese characters, write in hiragana and click F7 for conversion to Katakana. This works fine in the standard applications, like LibreOffice, or Firefox, but does not work in Qt applications, as is Anki.
Qt is a cross-platform application framework that is widely used for developing application software with a graphical user interface (GUI). (from wikipedia)
To fix this I stumbled upon
this solution:
$ sudo apt-get install ibus-qt4
Restart Anki, and it works.