Some people claim that Arjun is the incarnation of Lord Vishnu. But is it true?
In Mahabharata: Vana Parva: Arjunabhigamana Parva: Chapter 12, Lord Krishna himself says:
"Vaisampayana continued, 'Having addressed Krishna thus, the illustrious Pandava, who was the soul of Krishna, became dumb, when Janardana (in reply addressed that son of Pritha) saying, 'Thou art mine and I am thine, while all that is mine is thine also! He that hateth thee hateth me as well, and he that followeth thee followeth me! O thou irrepressible one, thou art Nara and I am Narayana or Hari! We are the Rishis Nara and Narayana born in the world of men for a special purpose. O Partha, thou art from me and I am from thee! O bull of the Bharata race, no one can understand the difference that is between us!'
Nara-Nārāyaṇa are considered incarnations of Lord Vishnu:
Text 35: These two sages, Nara and Nārāyaṇa, were the direct personal forms of the Supreme Lord.
In Śrīmad-Bhāgavatam (Bhāgavata Purāṇa) » Skandha 11: General History CHAPTER FOUR: Drumila Explains the Incarnations of Godhead to King Nimi, Nara-Nārāyaṇa is listed as incarnation along with other incarnations such as Hayagrīva, Nṛsiṁha, Vāmana, Paraśurāma, Rāmacandra, Krishna, Buddha, and Kalki etc.
Thus, Arjuna is the incarnation of Lord Vishnu (Vishnu --> Nara --> Arjuna). On a side note, Arjuna is also considered incarnation/son of Indra (What were the previous births of the characters of Mahabharata?).