First, since you're older than a day old when you start playing, your "born on" date should technically be several years before the start of the Combine. For this reason, many people keep track of that in their profile.
Although there is no way to track your character creation date, we do show you your account creation date on the "Account Settings" page.
Actually I have a question now. Does that join date apply to the current character you have, or does it apply to the join date of your first character? I ask because I've had 3 characters, and I'm curious to if it applies to my first or 3rd one.