With all due respect to SpaceLawyer, comparing the ISS to an embassy is not accurate. It would be more accurate to compare the ISS to an aircraft. Under the 1944 Convention on International Civil Aviation, articles 17–21, all aircraft have the nationality of the State in which they are registered, and may not have multiple nationalities. However a U.S.-registered aircraft outside U.S. airspace is not considered to be part of U.S. territory. A child born on such an aircraft outside U.S. airspace does not acquire U.S. citizenship by reason of the place of birth. On the other hand, "Comments on the applicability of the 14th Amendment to vessels and planes, are found in Gordon, Immigration Law and Procedure, Part 8, Nationality and Citizenship, Chapter 92, 92.03 (New York: Matthew Bender, 2007). This volume states:
“The rules applicable to vessels obviously apply equally to airplanes. Thus a child born on a plane in the United States or flying over its territory would acquire United States citizenship at birth.”"
So, the question then becomes where was the ISS when the baby was born? Over the US? That may be a factor, but I would defer to SpaceLawyer on whether or not US airspace extends to the orbit of ISS under the law. If it does, then most likely the situation is the same as if a Russian mom delivers a baby on a United flight over Wisconsin: the baby is American by jus soli. If not, then the situation is that of a Russian mom delivering a baby on a United flight over international waters, and the baby would not acquire US citizenship. He/she would be Russian.