I assume you mean the Rust Monster's antenna attack.
Sure, that's what it's for. There's no hit point damage from the antenna attack, only the rust effect. As for a carried weapon, it depends on how it's being carried. That dagger in the bottom of your pack ? Probably can't be touched without destroying the pack first. That throwing axe hanging exposed on your belt ? Fair game.
In any case, unless the object has been dropped on the ground (and is therefor unattended), there's a DC 15 reflex save.
I think armor and shields are legal targets for the rust monster's antennae touch attack which causes the touched object to rust. It should be able to make a full attack including a bite attack and a touch attack. Trying to adjudicate whether its rust attack hit armor/shield/sword is difficult. Since the creature isn't very intelligent and is neutral hungry for metal it would probably go after things in what it views as the biggest meal. YMMV.
Its this line the Rust Monster Rust Attack description that's throwing me off...
A rust monster never provokes attacks of opportunity by attempting to strike a WEAPON with its antennae
...so I was under the impression that maybe they could only attack weapons with this, rather than armor/shields.
At worse this implies that attacking the weapon with the antennae is like performing a sunder. Without improved sunder you would normally provoke an attack of oppurtunity for this, but it says the rust monster doesn't. I personally interpret this as the antennae is a melee touch attack not a combat maneuver so it doesn't provoke, and it just so happens on a successful touch is causes rust. I would say, that this applies to shield and armor as well, it doesn't make sense to provoke when attacking shield or armor but not weapon.