I don't think there is any OOTB web script. You can write your own webscript backed by Java or Javascript.
Similar question can already be found in the forum:
https://community.alfresco.com/thread/242495-how-to-get-how-many-folders-and-sub-folders-are-present...
Its better to search the forum before creating a new question.
~Abhinav
(ACSCE, AWS SAA, Azure Admin)
