Is Agarbathi business acceptable in Islam (halal or Haram)

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

It is permissible to sell incense and other types of fragrance. In fact, trading in fragrance is among the best types of trade. Fragrance is among the worldly things that were made dear to the Prophet, sallallaahu ‘alayhi wa sallam.

Anas narrated that the Prophet said: "In this worldly life, two things have been made dear to me: women and perfume, and the prayer is the comfort of my eyes." [Ahmad and An-Nasaa’i - Al-Albaani classified it as Saheeh (sound)]

Also, the Prophet, sallallaahu ‘alayhi wa sallam, said: "The example of a good companion (who sits with you) in comparison with a bad one, is like that of the musk seller and the blacksmith's bellows (or furnace); from the first you would either buy musk or enjoy its scent while the bellows would either burn your clothes or you get a bad nasty smell thereof." [Al-Bukhari and Muslim]

In any case, there is nothing wrong with selling incense or buying it in general.

Allaah Knows best.