This use names the sign itself, not a person. It is uncountable, so it normally takes no a and no plural s — the s is part of the spelling. It is a proper name, so it keeps its capital letter wherever it sits in the sentence. You meet it in horoscopes, apps and birthday talk, usually with the dates or with the picture of the two fish.

Here the name of the sign is used for a person. This one is countable, so it takes a: I am a Pisces, she is a Pisces. That little a is the whole difference between talking about the sign and talking about a person born under it. It is everyday social talk, not technical, and it says nothing more than when the person was born.