Can you give a cat penicillin for a respiratory infection?

You are far better advised to visit the vet and get a prescription that is made for cats. Feline metabolism is different enough from human that drugs that are harmless to humans will kill cats; plus the necessary dosage is very different, even for those drugs that are used for cats. Typically, your vet will prescribe Clavamox, which contains amoxycillin, a member of the penicillin family which is still somewhat effective.