Why does Gragas have rope around his arms?

He uses them to help finding veins to inject his brew into.

Because Caitlyn wears lots of belts....for no reason at all!

https://en.wikipedia.org/wiki/Pra_Jiad

Culture yourselves.

As a matter of fact, in Gragas' Universe page, there's a piece of concept art of how a revised & modern Gragas could potentially look like, in which he doesn't have ropes:

http://universe-meeps.leagueoflegends.com/v1/assets/images/image-gallery/gragas_concept.jpg

why not

Probably something along the lines of how how they just got stuck on when he was drunk and rumbling or somethin.

to nerf his infinite drunk power