Exact birth dates go unmentioned in the story and it is noted that nothing special is done for the kids in Battle School when they officially turn a year older.
All we know is that Ender is 6 years old when he enters Battle School and 10 when he leaves.
Back on Earth, however "Valentine celebrated Ender's eighth birthday alone," (122). She builds a small fire and wills the smoke to reach him all the way in Battle School. She feels like everyone has forgotten about Ender, which insinuates that even his parents no longer mention his birthday on Earth. It is not mentioned in Battle School, so it is certainly not celebrated.
Ender's birthday is not recorded in the way birthday's are normally recorded. He was born in 1191 BSC, or Before Starways Congress.