Perhaps the best known Hindi word beginning with A, and widely used in other languages, is 'avatar'. This comes from the Sanskrit avatara, which was used to refer to different gods in Hinduism and then came to be associated with the idea of 'incarnation' (as in the Hindu belief in reincarnation in different bodies). The word is also connected with the idea that the divine is present in human form or human life.
In English the word can have a similar meaning, though now it is often used to mean an icon or figure used to represent a person in a virtual environment (as in the film Avatar).
Another word of Sanskrit origin used in English is Aryan, which originally meant noble, good etc, but has come to be associated with offensive theories about racial purity and so tends to have negative connotations in modern English.
You can find a list of Sanskrit words used in English here.