You need to be SUPER careful when offering a pet for free (well, anytime you're rehoming a pet, of course, but the word "free" seems to attract a lot of bad guys). Check vet references, check with their landlord, etc. Free cats frequently end up as fighting dog bait or snake food or lab specimens .
Totally agree with Willowy......Researchers will pay up to 120 dollars for cats to do research on........Have you contacted your vet? Or other rescue groups?
ETA: It's late and I did not check the date the thread was created before posting, and know the OP is long gone, but decided to leave the post in case it might help someone looking in a similar situation.
Welcome. First of all, this is an international forum. Unfortunately it is very unlikely that you will be able to find anyone here to take your cat.
I agree with everyone who is advising extreme caution in giving a cat away for free. If you are determined to do this, you really have to use EXTREME caution. At a minimum, even for non-kitten, I'd ask for a minimum $25 fee, or if you are more comfortable a donation to a charity. If you want you can offer to refund the fee on proof that the cat was taken for the vet, but this is usually easier pre-spay or neuter as there'd be no reason to take a healthy 9-month old kitten to the vet for around 6 months when the rabies would need to be renewed and an annual physical would typically also be preformed. In any case, the fee should be high enough that the average person would need to consider it, however briefly.
If you do feel you need to offer the cat for free ( I know how hard finding a home for one can be, even a tiny kitten) you should definitely do as Willowy suggests. Ask for vet references (and actually call them) take a detailed pet history, and speak to them at length about previous pets, why they want a cat, views on declawing, what would cause them to rehome the cat, etc.
If you don't mind my asking, why do you need to rehome her? It is possible that if you talk to us in more detail about the issues you are having in keeping her, we'd be able to help you find a way to do so. Her best chance at a happy and healthy life really probably is to stay with you.