You can also see it from your game console.  Just log into Elite and at the bottom of the first page that comes up, you will see how many invites are waiting for you.  Click on that and you can pick which one to accept.  If your having trouble getting the invite, you can go to the clan's elite page and use the apply feature.  Then the clan leader can just accept your application and you're in.

Just click on the invite tab anyway. I have 2 clan invites and its says i have 0. So just click it just incase