Options:
What colour are you?
Where are you from?
Where are your parent's from?
What's your ethnicity?
What's your background?
What race are you?
Do you have any X in you?
Are you X?

What is the right way to ask?
Is it rude or offensive to ask?

What do you think?

English script:
http://thedailyenglishshow.blogspot.com/2010_03_09_archive.html

英文スクリプト＋日本語訳＋番組詳細
http://tdes.blog120.fc2.com/blog-entry-786.html

Show 1191 Tuesday 9 March
The Daily English Show
http://www.thedailyenglishshow.com/