Medscape states that while pets were once suspected of harboring strep throat in households that had frequent outbreaks, the variety of strep that cats carry, called "Streptococcus canis," does not cause pharyngitis (also known as sore throat) in humans. Medscape cites a study that found no presence of strep throat-causing bacteria in family pets and concludes that there is no evidence of pets being a vector of human strep throat.
This does not mean that strep does not cause respiratory illness in cats. According to PetMD, S. canis affects the respiratory system of both cats and dogs. PetMD reports that the symptoms of S. canis infection in cats include difficulty breathing or swallowing, coughing and pneumonia, all common signs of respiratory distress.
This also does not mean that S. canis cannot infect humans. The bacteria is occasionally found in medical cultures taken from humans. In a study by Galpérine Tatiana, S. canis accounted for only 1 percent of all streptococcus bacteria isolated from human patients. S. canis is much more common in cats; the Winn Feline Foundation states that the bacteria is found in approximately 10 percent of cultures of the nasal cavity taken from cats with upper respiratory tract infections.