How to add custom sort order to a taxonomy field list?
The Taxonomy Term Reference Sortable Widget module appears to meet your requirement. Once installed, the module will provide a widget that can be selected for a taxonomy term field via its widget type panel. (Admin -> Structure -> Content Types -> My Content Type -> Manage Fields -> My Field -> Widget Type).

If you have a lot of different terms available this may not be a good choice because it displays a full master list of terms from which you select and order those you need. It does not have an option for using autocomplete to build the set.