There is the Jazzy Spell Check API. Unfortunately it is a bit old, and despite the efforts of some people to revive the project (see the "forum" at the project's site), they have been unsuccessful. The API works and is used as the spell checker in current projects (IntelliJ IDEA spell check plug-in, Eclipse spell check plugin, etc).
Jazzy is the only opensource / free spell check API I am aware of. There might be some others. There are some other commercial products available. If you ask my good friend Mr. Google about Java Spelling API, he'll provide you with a bunch of resources and links.
I personally am not sure if anyone has created an Arabic dictionary for the Jazzy API, but Google should be able to help you find answers to that as well.