Well, I've never heard of ringing in the ears being a possible side effect of finasteride, but when you're taking a medication, you have to realize that everyone is different. Even if finasteride doesn't commonly cause ringing of the ears, maybe it does in you. If it becomes troublesome, the best thing you can do is go to your doctor and maybe he can help you to rule out potential causes. If you're on any other medications, it could be one of those too. If it's not too bothersome, just keep an eye on it for the time being.
If in the future you do have good reason to suspect that it's finasteride, you can try stopping it for a few weeks to see if you notice any difference.
Good luck.
Jeremy