Is June 9th 2013 a Orion sign?

If you are born June 9th 2013 does that make you fall under Orion sign? I know Orion sign is around June 7th I just found out there is a Orion sign today.

I know most people know the main 12 signs and June has Gemini and cancer but I saw in some days of June it's Orion sign.

I asking because my cat gave birth June 9th 2013 one of the kittens I named Orion if his sign is Orion that'll be cool :) I named him Orion the day he was born

Thanks for any answers I get.