Yes, Anki collections and decks (.apkg, .anki2 files) can be imported for use with AnkiApp. NOTE: card content will be imported, but existing review statistics (study progress) will not be imported. These files can be exported from the Anki desktop application. To do so, open the Anki application and follow these steps:
From the main deck list screen:
From the export dialog:
The exported deck package (.apkg) can then be imported using the AnkiApp import tool at: http://import.ankiapp.com.