✔ 最佳答案
Are you asking this as a conversational question, eg. to some friend you just meet? Or are you using this as a question in a survey?
If it's informal:
Is any of your parents or grandparents from Asia?
Do you have any Asian background?
Where are you originally from?
If you want to, you can say
Do you have any Asian ancestry?
I think this is closest to what you want? Though it doesn't sound as natural as the other suggestions quoted here. Sometimes translation doesn't go word for word.
Formal:
Do you have any ancestors of Asian origins?
See for reference:
http://www.statcan.ca/english/sdds/instrument/4508_Q1_V1_E.pdf
http://www.statistics.gov.uk/about/Classifications/ns_ethnic_classification.asp
Please also note that for some people, especially Americans, race/ethnicity is a very private and sensitive issue. Some may feel offended that you ask such question and may wonder if you are discriminating. If they are mixed, some are proud of their various ancestries, some are not.
For example, if you ask someone "Where are you originally from?" most people will gladly give you an answer. But someone 100% Asian may say I am from Boston, because his grandparents moved to US from Hong Kong and he was born here. He may feel upset that because he doesn't look white, people don't consider him American, even if he's third or fourth generation born in U.S.
Probably more information than you ask for, but just want to say, please be careful when asking this question, because you may get very negative reaction.