Here are some of the latest statistics available from the United Nations High Commissioner for Refugees (UNHCR), giving their count of US citizens who are now refugees / applying for asylum.
However these numbers do not include American applicants who’ve been refused asylum. Some we know of have been stranded in legal limbo for as much as ten years, but still refuse to return to the US, out of fear for their safety. (You can view the full UNHCR Statistics at this link: http://www.unhcr.org/52a723f89.html)
UNHCR Statistical Yearbook - Statistical Annex
Refugees & asylum-seekers by country of origin
Country Applicants Total refugees
of origin waiting & applicants
USA Refugees for asylum for asylum
(2012) 4453 432 4885