There are more than one artist with this name:
(1) Austin Santos, reggaeton style singer.
(2) Francisco José Arcángel Ramos, flamenco singer.
(2) Arcangel is also a hard rock/industrial metal band from 70's.

More in depth:

(1) Austin Santos, best known as Arcangel, was born in 1985, in the city of New York to Dominican & Puerto Rican parents.
His mother moved to Puerto Rico in the early 80s to realize her dream of singing by joining a Merengue group known as Las Chicas del Can. Austin met a young man known in reggaeton as "De La Ghetto" and the two began working together.
"Arcangel & De La Ghetto" although they are relatively new artists, have done well so far with hits like "Agresivo", "Sorpresa", and "Mi Fanática". They gained fame relatively quickly. Many people who have been listening to reggaeton since its beginnings in the early 90's criticize the duo, particularily Arcangel for being "cocky" and trying to engage older more established reggaeton stars in rap battles.
Other people argue that his attitude is warranted because the duo is well known without having released their own album.
A recent tiraera (rap battle) occured with another duo, Jowell & Randy. You can check out some videos of them talking about each other on Youtube!

(2) Francisco José Arcángel Ramos (Huelva, 1977) is a Spanish Flamenco singer formerly known as Arcangel.

He began in 1987, but he is not well known until 1998 with his participation in X Bienal de Flamenco de Sevilla. From this moment, Arcangel sing for dance to famous dancers like Javier Barón, Eva Yerbabuena or Israel Galván and he also work with Vicente Amigo, actually one of the best guitar players.

His first solo album was entitled Arcangel (2001). With this album, Arcangel won several regional and national prizes, like Premio Andalucía Joven 2002, Premio Nacional Flamenco Activo de Úbeda or Premio Giraldillo.

The two last albums has been La calle Perdía (2004) and Ropavieja (2006).