There are lots of different ways to ask for permission to do something:
Can I ___? May I ___? Would it be all right if I ___? Would you mind if I ___?
In the situation above, you don't need to be too polite. So "Can I ___?" is a good choice. Use "Can I ___?" when you want to do something that doesn't cause trouble for the other person. It's also good for asking questions of people that you're close to or on a similar social level with.