Carl Denham: I'm someone you can trust, Ann. I'm a movie producer.
Carl Denham: It wasn't the planes...it was beauty killed the Beast.
Carl Denham: Bring the tripod and all of the film.
Herb: Want to switch to the six-inch lens?
Carl Denham: The wide-angle will be fine.
Bruce Baxter: I'm just an actor with a gun who's lost his motivation.
Carl Denham: There are thousands of actresses out of work in this city. Somewhere out there is a woman born to play this role... A woman who will journey into the heart of the unknown... Toward a fateful meeting that changes everything.
Jack Driscoll: Actors. They travel the world and all they see is a mirror.
Answer: I assume you mean, could the building take his weight, not whether an ape would really have the ability to climb a building (if that's what you mean, then it's definitely yes...apes are great climbers). Assuming Kong is proportionally as heavy as normal-sized gorillas, which tend to be in the area of 160kg (~350lbs), then he weighs over 80,000kg (89 tons, give or take). The average human weighs about 62kg, so that's about 1,300 humans, and the capacity of the ESB is over 13,000. So, assuming the building is mostly, or even half, empty while a giant gorilla scales it, the building could handle his weight.
Keep in mind, though, that the weight allowance for the building assumes people on the floors of the building, not climbing on the outside. The outer structure of a building isn't designed for massive creatures climbing on it. While the building as a whole would likely survive, there would be significant damage as Kong would be breaking windows and pulling stone off it as he made his way up.