According to the US census:

"White" refers to a person having origins in any of the original peoples of Europe, the Middle East or North Africa. It includes people who indicated their race(s) as "White" or reported entries such as Irish, German, Italian, Lebanese, Arab, Moroccan or Caucasian.

Additionally, people who reported Muslim (or a sect of Islam such as Shi'ite or Sunni), Jewish, Zoroastrian, or Caucasian as their "race" in the "Some other race" section, without noting a country of origin, are automatically tallied as White.