How many exotic items can I use at once?

Solution 1:

You can equip two exotic items: one weapon and one armor.

Different sources: 1,2,3

Whenever you have an exotic weapon equipped, other exotic weapons in your inventory will appear disabled (dark yellow) and you're unable to equip them until you unequip the one you have equipped.

The same holds for exotic armor items, other exotic armor items will appear with the same dark yellow cast and you will be unable to equip them.

Solution 2:

Nope only one weapon and one armor. So pick and choose. Just because you can buy one piece of exotic gear doesn't mean it's worth it, you may want to wait to find or buy a piece that suits your play style and compliments your guns and armor. Trust me I learned the hard way