This feature is not available. You can just short them by clicking on Name or Path.

BTW what you want to do by rearranging them?

I want to choose a more prioritized item from this list. This item should be first, but the sometimes prioritized item can be the last.

So one better solution will be to create a ContentReference type property (as we did in our one of the project) to select category (as allowed type) and use it. What you say?

I take it you want one additional category to prioritize other than the primary category?

If not you could just assign your preferred category as the primary category for the entry - moving the entry to the preferred category will change the primary category for you in that case. 

I believe the order in that list is determined by SortOrder in NodeEntryRelation. While it cannot be arranged in the Ui, you can set it by code (using IRelationRepository)