"Do you know?" is correct as a question.
"Did you know?" is more often used in speach. This question is also correct.
At first "Did you know?" seems to be using the wrong tense, but in fact it is simply asking "did you knew before now?".
When people ask "Did you know that London is in England?" they are asking "Did you know that London is in England before I told you?
If this is unclear, I will explain in a different way.
Hope This helps.