I know there's a little check box for when you are about to post a finished anim, but I don't think there is a way to private already existing anims.

Although, I've been on this site for just a few days now, so I don't know 100% for sure.

When uploading an animation, before you click upload, click a little box with a checkmark in it called "Make this animation public". With the check, it's public. Without it, it's private.