Depends on which type of media you look at. He wasn't an avenger in the movie but he's been an avenger in some comic books (not sure about official marvel ones).
I was told that he was an avenger, and that he was part of the avengers in the comics, but he wasn't in the movie because he's owned by Sony. Not saying that I'm right, that's just what I've been told.
Do you people even read comics?!? :| Spidey is an Avenger! And as for that pic, the Avengers movies are "real" avengers movies, as marvel has stated, the Cinematic universe is a universe of its own, therefore it doesn't have to follow a specific story line. All the movies so far have been a combination of the 616 and 1610 universe (mainstream and ultimate). Trust me, I've done my research.
Read a comic book
P.s. I do read comics