No, it is not built into Realm for functionality.
However, there are ways your app code can make this happen: https://stackoverflow.com/questions/30028282/realm-and-auto-increment-behavior-android
Even though Realm uses tables and has relationships with other tables, it is not your traditional SQL type of database. You do not to use foreign keys and reference fields by ID. With that in mind, I would assume that you might not even need an ID field in your RealmObject so therefore, do not need to do auto incrementing.
In one app I developed, I did need some sort of ID to make a Realm object unique over others. What I did was made a "realm_id" property, made it type String, and set it using UUID to make it unique. Much easier then actually using Int type with keeping track of the next ID to use.