He may have a broken upper arm (humerus) or a dislocation.
Depending on the extent of the injury it might be possible to surgically repair either condition.
Alternatively if the problem cannot be repaired or is too costly for you to repair the leg can be amputated. Cats do not have collar bones so the leg just sits on muscle tissue and is held in place by that and ligaments.
You can see a diagram of the cat bone anatomy here
Click on the picture to enlarge it.
Because a cast cannot be put on the area to control movement of bone surgical repair is the method of choice, to pin or plate broken bones, or to put the joint back in place and then hold it with a strip of tissue or material so it can heal.
An x-ray may tell you a lot about what is going on.
If cash flow is an issue in getting care you might check out Care Credit
A credit card company for health care, including veterinary care.
"With a comprehensive range of plan options, for
treatment or procedure fees from $1 to over $25,000, we offer a plan
and a low monthly payment to fit comfortably into almost every
They have a zero interest program if you pay within a certain time frame and they list the vets who work with their product.
Hope this helps you!