If you need to only replace one tire on your car because you can only afford one tire at a time then you can do so.
But most tire repair shops will not replace only one tire and will only replace 2 tires or all 4 tires at once if the others are bad.
This is due to liability issues with their insurance and it's what a tire shop told me before.
However you can take the tire and wheel off the vehicle and bring that one tire and wheel into a tire shop and have then replace it with a new one.
They will change the tire on one rim if you bring just the tire too them.
If possible you should at least replace 2 tires at the same time so that they wear evenly and for safety reasons as well.
Make sure the tires are the same tread and size as well for safety.