Are you using APEX data loading wizard? Notice that four pages are created when we use APEX wizard, browse, map, validate and action.
On first page, add a select list for user to select month. Suppose he select January and the item name for select list is "P1_MONTH".
Now you may follow two approaches here.
1. You may add a after insert trigger on your table.
after insert for each row,
set month = :p1_month.
2. On fourth page of your data loading wizard, after insert process, add a plsql process,
set month = :p1_month
where month is null;
This obviously assumes that all previous data if any , already consist of some value in month column.