The response has the order the results were returned in, but is it possible to set the order in the request?
It is possible to set the limit and offset when executing the Get a Folder’s Items, but this functionality seems incomplete if the order can't be supplied.
As per the documentation example, a limit and offset URL parameter can be set.
curl https://api.box.com/2.0/folders/FOLDER_ID/items?limit=2&offset=0 \
-H "Authorization: Bearer ACCESS_TOKEN"