At least two oracle mysteries contain revelations letting an oracle use his Charisma modifier instead of his Dexterity modifier to compute his AC (the mystery lore has the revelation sidestep secret and lunar has prophetic armor). I want a revelation like that, but I don't want to take the mysteries that make available that kind of revelation. Is there a way for an oracle to get an off-list revelation?
By first party (made by Paizo) RAW, no there isn't.
Extra Revelation requires that you have the prerequisites for the extra revelation you're getting (which means you have to have the appropriate mystery).
Ring of Revelation also explicitly states that you must have the appropriate mystery to use the revelation contained in the ring. (And the commentary on the sidebar is an unofficial (albeit from the Creative Director) statement saying that Use Magic Device would not allow you to fake having that mystery prerequisite)
There is, however, a third-party feat that would allow you to do this:
Strange Revelation enables to you to use Extra Revelation to acquire a revelation from a mystery that isn't your own.
Third party stuff is a grey area, and something I recommend you ask your GM about before you take it.
TLDR: No, but third party content allows it.
The Ring of Revelation will allow you to do this. The original entry only limits its use to Oracles.The creative director has made two comments on it, the latter of which isn't reflected on d20pfrsd:
Use Magic Device will let you trick an item into thinking you're a different class... but it does not grant the POWERS of that class. The way the ring of revelation is worded pretty much means you HAVE to be an oracle (aka you have to meet minimum level requirements in class abilities granted by the oracle class, since the powers granted directly affect that ability rather than grant you NEW abilities). Furthermore, the ring specifically says that it has no effect if worn by a non-oracle.
SO. Best case scenario, you could Use Magic Device to trick the ring into activating, but if you don't actually have class levels in oracle, the ring will do nothing more than take up a ring slot for you.
Can an Oracle of a given mystery use UMD to emulate a different mystery in order to access the revelation coded into the ring?
For example: Suppose a Nature oracle who finds a ring of revelation containing "Sacred Council" from the Ancestor mystery. Can s/he use UMD to emulate the Ancestor mystery class feature and thereby access the "Sacred Council" revelation from the ring (assuming s/he continues to make the requisite UMD checks every hour to continue emulating the Ancestor mystery)?
from: James Jacobs
Yes. That's using the "emulate a class feature," in this case, the class feature of having the Ancestor mystery. I guess, in theory, you could do that if you were ANY class, though. Which may not be the way I've interpreted the ability before.
Strictly RAW, there are two versions of Ring of Revelation. One is from Ultimate Equipment and contains the line about not functioning under UMD. The other one is from Advanced Player's Guide and only says that it doesn't function for non-Oracles. There is a similar situation with Snowball: technically, Paizo didn't nerf the spell from People of the North, but rather published another spell with the same name.
Thus, just get the APG version of the ring and have fun.