The advert stipulates that the post is only open to applicants not involved in "sexually deviant behaviour".
It says this must be proven with a doctor's certificate.
Critics have accused the government in effect of destroying the futures of creative young LGBT people.
They have been barred from serving their country because of their sexuality, campaigners say.
Gay sex is not illegal in Indonesia, and the world's largest Muslim country has a vibrant transgender culture.
It is a tradition which is broadly met tolerantly by the Indonesian public.