Hello I am Dr. Joey. Thanks for trusting me to help you and your pet today. I am a licensed veterinarian with over 15 years of experience. I look forward to working with you.
I am sorry your cat is experiencing this but let's see if we can come up with some options.
My top worry with a limp tail is that he may have broken it at its articulation into the spine. If he is able to twitch the end of it at all, then this is unlikely. And, if he can even slightly arch it up at the base or twitch it a bit, then I would suspect trauma or an injury like a bite (abscess, infection) but you should see a swelling develop if there is a bite or trauma causing this. The good news if he can move it at all is that this should get better over time, although he may need some help from us along the way (medications).
At home, unfortunately, there is not a lot you can do for this. However, it is not an emergency situation unless he is very painful and then I would recommend have him seen. If it persists into tomorrow, then I recommend you have his regular veterinarian examine him to determine if (s)he thinks this is due to trauma or a fracture. An X-ray may be needed to make the fracture diagnosis. In the worst case scenario if this is fractured, then he may need to have his tail amuputated since this tends to get soiled with feces/urine and sometimes cats chew on the tip of the tail and traumatize it because it can have shooting/tingly pain the cat doesn't understand.
I am at a point I need to know what questions you have. I hope that the information I provided has been helpful.
Please let me know if for any reason you need further clarification, have more questions, or were expecting a different type of answer.
My goal is to provide the best answer possible prior to you leaving a feedback rating.
If you received all the information you needed, then kindly submit a rating.