The only two scriptures have have remotely any relevance to birthdays are:
Job 1:4: "His sons used to go and hold a feast in the house of each one on HIS DAY, and they would send and invite their three sisters to eat and drink with them."
and Romans 14:5,6: " 5One man regards a certain day above the others, while someone elseconsiders every day alike. Each one should be fully convinced in his own mind. 6He who observes a special day does so to the Lord; he who eats does so to the Lord, for he gives thanks to God; and he who abstains does so to the Lord and gives thanks to God.…"