Refugee Crisis in Iraq Act - Directs the Secretary of State (Secretary) to establish processing facilities in Iraq and in countries in the region for eligible Iraqis to apply and interview for U.S. admission as refugees or as special immigrants.

Includes among refugees of special humanitarian concern: (1) Iraqis who were employed by, or worked for or directly with the U.S. government in Iraq; (2) Iraqis who were employed in Iraq by a U.S.-based media or nongovernmental organization or an organization that has received a grant from, or entered into a cooperative agreement or contract with the U.S. government; (3) spouses, children, sons, daughters, siblings, and parents of Iraqis who worked for the U.S. government or who are special immigrants; and (4) Iraqis who are members of a religious or minority community and have close family members in the United States. Authorizes the Secretary to identify other priority groups in Iraq.

Authorizes the Secretary of Homeland Security to provide special immigrant status to an otherwise admissible Iraqi national (and spouse and children) who was employed by, or worked for or directly with the U.S. government in Iraq for at least one year in or after 2003.

Directs the Secretary to: (1) establish in the U.S. embassy in Baghdad, Iraq, a Minister Counselor for Iraqi Refugees and Internally Displaced Persons; and (2) designate in the U.S. embassies in Cairo, Egypt; Amman, Jordan; Damascus, Syria; and Beirut, Lebanon a Minister Counselor to oversee U.S. resettlement of persons considered refugees of special humanitarian concern.

Directs the Secretary, with respect to each country with a significant population of displaced Iraqis, including Iraq, Jordan, Egypt, Syria, Turkey, and Lebanon, to: (1) consult with other countries regarding resettlement of the most vulnerable members of such refugee populations; and (2) develop mechanisms in and provide assistance to countries with a significant population of displaced Iraqis to ensure their well-being and safety in their host environments.

Amends the Immigration and Nationality Act to permit a qualifying Iraqi applicant for asylum or withholding of removal whose claim was denied on the basis of changed country conditions to file for reopening of his or her claim.