For one you should stay as far away from his shots as you can. Getting buckshot in the head will kill you like it did katarina. Make sure you never stand in the powder of his Q, it's ok to get hit by the bullet but it's the fire that hurts like a bitch and woe betides anyone that got hit by both. W is the same but watch out for his E, as he gains armor and closes in on you. His ult has made him a little more slippy as he backs away then it's shot.
TL;DR: Dodge Q, attack during reload, Watch out for E and Ult now pushes him back a bit. And for god's sake don't be close to him as he will OHK you.
I just played against A Graves top lane as Rammus and I managed to play safe against him. So anytime I was trading him I was popping my W and rushed Thornmail to counter him. having a lot of armor and health will help a lot and you should watch out for when True Grit is up as he is as tough as rammus in that state. More or less you really need to focus him and make sure he doesn't screw you out. he doesn't have a proper escape apart from E.