There are multiple ways to look up someone's birthday for free. The first method is to use social media and look at her profile. Another method is to take a look at her calendar if she has one. You can also privately contact close family or friends.
According to Reference.com, "there are several sites on the Internet that will keep a birthday database of the people that you know." However, take caution when using these sites. Some of them may be free and safe to use, but others may prompt you to pay or may use your information for spamming purposes and possible identify theft attempts.