First of all, it is irresponsible to adopt any pet if your current financial situation is such that you cannot afford to provide for its needs, which includes regular veterinary checkups and the possiblility of medical emergencies or other medical costs if the animal turns out to be unwell. Especially in the case of a feral cat, your first act as a new pet owner should be to bring it to a vet to get it all its immunizations, including the rabies vaccine, and a health assessment.
As for the risk of rabies, rabies is transmitted in the saliva, and only transmissible after it is showing clinical signs. The most well-known method of transmission is through a bite by an infected animal, however, you can contract it in other ways such as through contact of infected saliva with an existing open wound.
Since you have said the animal does not have symptoms, and you have not mentioned getting bit, most likely your current risk is small or none. However, that said, I still recommend you contact a doctor immediately, as rabies is for all practical purposes one hundred percent fatal once symptomatic, and therefore all precautions should be taken, starting with getting an actual doctor's advice.
Furthermore, since we know nothing of the animal that bit it, and there is no test to determine if a live animal has rabies, it is impossible to say whether the animal has rabies or not. It is a greater than zero possibility the animal could develop rabies symptoms later.
It also seems irresponsible to me to release an animal because you're afraid it might have rabies, as if it does, you are now allowing the infected animal to go around spreading it, and also leaving it to suffer.
You should contact your local animal control services or a veterinarian about the procedure to deal with an animal with an unknown bite wound. The normal way that the possibility of a rabies exposure is handled is to quarantine the animal. How exactly the quarantine is done can vary. Some places use a special facility, others allow the quarantine to be done at home.
Therefore, I would say the most humane and responsible thing is to do is a proper quarantine and also attempt to rehome the cat with an owner that can afford its veterinary care.