Yes. Budha was Vishnu avatar. There are many budhists oppose this claim but many great budhists personality accepted the truth.
Thomas William Rhys Davids (Founder of Pali taxt society)
Budhism p 116-117:- "We should never forget that Budha was born and brought up a Hindu and lived and died a Hindu..........he was the greatest and wisest among Hindus."
Herman Oldenberg quoted in Ancient Indian Education :Brahmancial and Budhism by R K Mukherjee.
".......For hundred of years,movements of Vedas were in progress in Indian thought which prepared way for budhism"
Not only several indologists studied budhism but even Dalai lama the highest budhism personality today accepted it. He quoted in Elst Koenraad (2002)
"........When I say that budhism is the part of hinduism, certain people critisize me. But if I were to say that Hinduism and Budhism are different it would not be in conformity truth."
It is enough to prove budha as Vishnu avatar but I will provide some more proofs from scriptures. Many Hindus say that Krishna was ninth and balaram was eighth avatar of Vishnu and budha was not in the list but Garud puran separate both of them and says that balaram and budha were 20th and 21st avatar respectively. It gives the list as follows
Garud puran 1:1:-"His first incarnation was in the form of the eternal adolescent Sanat kumar and others who were all celibates and extremely virtuous.’
‘Lord Vishnu took his second incarnation in the form of a boar (Varah)**to protect the Earth from the mighty demon named Hiranyaksha, who had abducted her to Patal loka (Nether world). In his third incarnation as **Narad, he propagated the virtues of ‘nishkaam karma’ (performing one’s duties without bothering about the results). In his fourth incarnation as Nar-Narayan, he performed arduous austerities for the protection and propagation of Dharma or religiousness.
Lord Vishnu’s fifth incarnation was as Kapil, which he took to protect the Saankhya shashtra, which was on the verge of becoming extinct. He took his sixth incarnation in the house of Atri and Anusuya as Dattatreya with the specific objective of propagating the most secret Brahma vidya to worthy people. His disciples included virtuous souls like Prahalad and others. Lord Vishnu took his seventh incarnation as the son of Ruchi Prajapati and Aakuti and was known as Yagya deva. His eighth incarnation was as Rishabh deva- the son of sage Naabhi and Merudevi.
In this incarnation he established the norms for Grihashtha ashram, which later on became the guidelines for every householders. Lord Vishnu took his ninth incarnation as Prithu and ‘milked’(extracted) various nutrients (cereals, pulses etc.) from the Earth who had disguised herself as a cow and thus protected the populace from getting starved to death.
In his tenth incarnation as Matsya (fish),he protected the life of Vaivaswat Manu, who would not have survived otherwise. Lord Vishnu took his eleventh incarnation in the form of a tortoise (kurma) and held the Mandarachal mountain on his back at the time when the ocean was being churned. His twelfth incarnation was as Dhanvantari and thirteenth as the most enchanting beauty- Mohini to retrieve the ambrosia pot from the possession of the demons. He subsequently distributed it among the deities as the result of which they became immortal.
In his fourteenth incarnation, Lord Vishnu manifested himself as ‘Nrisimha’ (partly human and partly lion) and to protect his devotee- Prahlad killed the wicked demon Hiranyakashipu by tearing apart his abdomen with his sharp claws. His fifteenth incarnation was as Vaman (dwarf) in which he demanded all the three worlds from Bali-the most benevolent demon king and then sent him to Patal loka. In his sixteenth incarnation as Parshuram, he wiped out the whole caste of kshatriyas from the face of the earth for twenty-one times, as they had all become immoral.
In his seventeenth incarnation he was born as Vyas to Parashar and Satyavati and accomplished his mission of propagating the knowledge of Vedas by categorizing them into four parts. In his eighteenth incarnation he manifested himself as Sri Ram. His nineteenth incarnation was as Krishna and his twentieth incarnation as Balram. He will take his twenty-first incarnation as *"Buddha** to bring the mankind back to virtuous path by preaching against the rituals and proving that it is not proper for a seeker to get bound by them." Source :-https://www.wisdomlib.org/hinduism/book/the-garuda-purana/d/doc59291.html
Now I will provide some proof from budhists scriptures.
We all know that Vishnu is the supreme god and known as param Brahma.
Narayan Upanishad chapter two(https://i.stack.imgur.com/2qqGn.jpg)
Now budhists scriptures also Budha as Brahma.
Madhupindak sutta (The ball of honey):-
"He is the Eye, he is Knowledge, he is Dhamma, he is Brahma. He is the speaker, the proclaimer, the elucidator of meaning, the giver of the Deathless, the lord of the Dhamma, the Tathagata." Source:-
Note:- Tathagata is the name of budha. Budha also praised agnihotri. Wikipedia :-https://en.m.wikipedia.org/wiki/Pāli_Canon#Use_of_Brahmanical_devices
The Pali Canon uses many Brahmanical terminology and concepts. For example, in Samyutta Nikaya 111, Majjhima Nikaya 92 and Vinaya i 246 of the Pali Canon, the Buddha praises the Agnihotra as the foremost sacrifice and the Gayatri mantra as the foremost meter:
aggihuttamukhā yaññā sāvittī chandaso mukham.
Sacrifices have the agnihotra as foremost; of meter the foremost is the Sāvitrī.
Many budhists oppose the brahmin teachings while budha himself claimed that he was a brahmin.
The Suttanipatta Mahagavvva-Sundarikhardwaja sutta verse 3:-
" sundarikabhardwaj asked:-'are you a brahmin'
Budha replied:- If you say I am a brahmin and call nlme no brahmin then I ask you about savitti who consists three padas and twenty-four syllabus"
Here budha is admitting that he is a brahmin and he knew Gayatri mantra.
Dashrath jatak 461 page no. 82, budha said:-
"At that time the king Suddhodana 3 was king Dasaratha, >Mahāmāyā 3 was the mother, Rāhulā's mother 4 was Sītā, Ānanda was Bharata, and **I myself was Rāma-paṇḍita."**Source:-https://www.sacred-texts.com/bud/j4/j4025.htm
Many budhists like Wendy doniger says that Budha came before Rama and accepted that he was ram in his previous birth' i.e. he was Vishnu avatar.
Now what proof is left for accepting budha as Vishnu avatar?
Some people say that Budha mentioned in puranas was born in Bodhgaya while Gautama Buddha born in Lumbini. The answer is that Hinduism Call the knowledge as second birth. Budha got knowledge in Gaya so it is his birthplace.