"Wie lautet dein Geburtsdatum?"
Übersetzung:What is your date of birth?
I'm American and I would say "When is your date of birth?". I actually tried that first before changing it to "What is your date of birth?" and got it wrong. Both are just as correct the way I see it.
I also tried "What is your birthdate?" and that was wrong according to the green owl. It wasn't a suggested word on my phone's keyboard either, so maybe it isn't a normally recognized construction? People around here (Northeastern USA) will ask for that or "birthday" instead. I tried "birthdate" because I thought it would be a more direct translation of "Geburtsdatum", since "Geburtstag" is birthday. Asking "What/when is your birthday?" is more common than asking "What/when is your birthdate?" though. Someone filling out a Form for someone might be more likely to ask them for their birthdate.