How do I jungle Rammus in S3?
Slowly.
On a serious note: AS Marks (for better clearing speed with Machete), Flat Armor Seals, MR per level Glyphs, Flat Armor Quints, 0/21/9 (improved buff duration, faster Smite with Mastermind) or 5/21/4 (solves some mana issues, you still get some manaregen and improved Flash CD) or 0/25/4 (tankier).
Start with Machete, get Boots of Speed and Spirit Stone/Madred's asap (Madred's if you plan on selling them later on and you care about your early clearing speed, Spirit Stone if you plan on getting SotAG later, have mana issue and/or your first Golem was denied to you somehow); then get Philo Stone (only if you plan on getting Shurelya's, otherwise skip it), Tabi and rush Sunfire (this helps your clearing speed a lot) and Aegis. At that point what you should build is situational. Good items are Frozen Heart, Randuin's, Bulwark, Spirit Visage, Warmog's, etc...