Arjun was the third of Pandavas. His mother was Kunti. Who is the father of Arjuna in the Mahabharat is explained below in the story. She was married to Pandu. But Pandu could not have sexual union with Kunti because of a curse. Kunti due to her service to Sage Durvasa had got a boon that she will be able to summon a god and have children in him. Pandu requested Kunti to make use of the boon. Thus Arjuna was born when Kunti summoned Indra, the king of the Devas.
But as per social custom that was followed at the time of Mahabharata, Pandu is the father of Arjuna.