Sure, he was there for the first issue in September, 1963 (by Stan Lee and Jack Kirby) and helped to found the team....
Short lived membership
...but the Hulk left the team after a misunderstanding in Avengers #2 (November, 1963 by Lee/Kirby) with the Space Phantom....
Hulk the menace
...and that led to the Avengers finding Hulk's replacement (Captain America) and even a battle with the rest of the Avengers and the Fantastic Four (in Lee/Kirby's Fantastic Four #25-26 of 1964).
Hulk the guest
...as well as in Avengers #88 (May, 1971, by Harlan Ellison, Roy Thomas and Sal Buscema), wherein the not-so-jolly green giant meets fellow guest (and future Avenger) Falcon, then faces off against the menace of Psyklop (and the Avengers and others plot to rid the Earth of the Hulk, which goes into the Incredible Hulk #140 in June, 1971, wherein the shrunken Hulk first meets his lady love of Jarella...).
Hulk the returning member
...and in Avengers #100 (June, 1972, by Roy Thomas and Barry Windsor-Smith), wherein the entire team faces off against Ares and the Enchantress! (Avengers #1, #2, #5 and #100 are the only complete gathering of Avengers, as other members would usually be absent during other mega-gatherings).
Hulk returns a Defender
...and Hulk battled Thor (as he often did) but Hulk fought Thor as a member of the Defenders (with Thor as an Avenger), at least until the two teams gathered together to fight Loki and Dormammu at the end in this epic written by Steve Englehart with art by Sal Buscema on the Defenders parts and Bob Brown on the Avengers parts.
Hulk does come back to the Avengers
...but he doesn't stay for long, not like he did with the Defenders!
The Battle Settled
...it is with his fellow Defenders...
...and why wouldn't he?
Issue #1 by Tom DeFalco and Ron Frenz, issue #2 by Joe Casey and Max Fiumara, issue #3 by Roger Stern and Karl Moline, issue #4 by Jim McCann and Agustin Padilla and issue #5 by Fred Van Lente and Michael Avon Oeming all prove that the Hulk and the Avengers just don't get along!