I am a young student in California and I have developed a theory, which I believe might affect the scientific world, though, through fear of it being taken or wrongly affected by others, I have kept it to myself.
While Catherine does a great job of explaining your options below (from a business POV) I believe that it would help you and us if you were able to provide a bit more background on what space/area your theory is involved in & what your intentions are. There are many fields of science such as life sciences, behavioral sciences, physics, etc.
To say that you have a theory that you haven't shared with anyone and presumably haven't tested a bunch of times would probably not go over too well within the higher echelons of the scientific community. As an entrepreneur, I constantly tell other people that ideas (or "theories") don't mean much, but rather what you do with them does.
In very simple terms, if you'd like to be the first person to be documented as having this theory then there are things you can do like publish a book/article or even record a video/video blog and email it to yourself or your attorney. Doing this should time stamp your introduction of this information to the known world.
If you want to get real deep then keep reading...
Apparently, there is an interesting "theory" about theories themselves called "The Underdetermination of Scientific Theory" which basically says that a scientific theory can only be disproven and not proven: https://www.quora.com/Why-can-a-scientific-theory-only-be-disproven-and-not-proven
The same user on Quora goes on to say, "In practice, this distinction often turns out to be largely semantic. Theories are not proven, but "accepted", with the notion that we might retract that acceptance in the face of new data. But that's under-playing the fact that a good theory has been tested many, many, many times, and it's quibbling to act is if there's a serious chance that it's incorrect (especially if you're not actively working on a better theory that also explains just how the old theory managed to survive so long)."