Can you have strep throat without having a sore throat?

Possible: One can sometimes be virtually asymptomatic and carry the bacteria in the throat/tonsil etc. The carrier state is however is not very well defined, its more like a very mild case. Only a throat culture can prove this diagnosis.

Words matter: "strep throat" is the lay term for a symptomatic illness caused by the strep germ. Since 5 % or more people carry this germ in their throat without ever getting ill, most would ignore it unless symptoms were involved. The "carrier" is one of the reasons we see this type of infection passed around all year long.The carrier can pass it to someone who develops the illness.