There is only one way to join the cult. You have to be invited by the Emperor or the Empress. You can not join without an invintation from one of these two people. You may, however, approach one of them and inquire about it. This will usually lead them to give you an invite.
Once you have recieved the invite, you must present yourself to one or both of their excellencies to prove that you are worthy of joining the cult. The emperor or the empress will give you a task to complete. If you are able to complete this task then you pass and will then become a member of the cult.
If you are unable to complete this task, do not give up. You still have a chance to join the cult. You may have another cult member stand in on your behalf and vouch for your validity. He or she will have to perform the task for you.