Welcome to Fluther.
As a parent whose own children are already older than you I would say “Who cares if they get angry about something so trivial?”
If your parents are going to get angry because you cut your hair, then they have their focus on entirely incorrect things. (And if necessary, you can tell ‘em I said so – but I wouldn’t recommend that until every other discussion point has failed. “Because some random old guy on the internet said it was a good idea” is never a good argument. Never.) Among the universe of bad choices, rebellious acts and stupid experiments that you could do to that might harm yourself, or put others at risk or damage or in any other way make the world a worse place, “cutting your hair” is far, far down on that list. It’s a stupid thing for them to be upset about. Let’s hope that your parents are not that stupid or thoughtless.
Which is not to say that they won’t get angry. Who knows what sets some people off sometimes? People are crazy from time to time, and parents, apparently, even crazier than most others, for some reason. (I wouldn’t know; I was not a crazy parent and neither were mine. I was lucky, and I know it.) But as others have already noted, it’s too late to ask the question now about “will they”. They will or they won’t, and what does our opinion matter? That’s also a silly question – which is why your parents’ opinion still matters, because obviously you also have a lot of growing to do, and to “learn to think before you do.”
All that is said by way of preface, and to help you to marshal any arguments that you might need – polite arguments, please; quiet and thoughtful ones only, okay? – in case your parents do take offense for whatever odd reason.
So: Just in case, here are the reasons why “it should be okay”.
You’re at an age when you’re testing boundaries, trying to find an identity, to find your “look” and all kinds of other things that are normal, natural and healthy for a child to do. “Messing with your hair” is one of the safest, least rebellious and least consequential things that you can do at this age. It’s not going to hurt you or anyone else. (As long as you don’t leave the cut ends as a mess for someone else to clean up, that is.)
In fact, if your parents get upset, then it’s a good time for you to act more maturely (more maturely than when you cut your hair on an impulse, anyway, and only then wondered about the consequences), listen to them quietly; don’t shout or argue loudly; accept their criticism with grace, and hear them out completely. Only then should you start to counter-argue (quietly, with logic and thoughful statements, based on facts that you can prove, and always respectfully) and impress them with how grown-up you can be (especially after you’ve already demonstrated what a kid you are – oh, well, that’s okay: you are a kid, after all).
If all else fails, when things have quieted down, you can always ask them “Do you know the difference between a good haircut and a bad one?”
Answer: sʞǝǝʍ oʍʇ.
Good luck. Let’s hope they even notice, right? That would be even worse, wouldn’t it, if no one even notices. Oh, let’s not go there…