[Cowboy Bob]

Under the law (I think...) The US citizen sperm donor has to marry the surrogate mother in order to even have a chance at citizenship.

[billakay]

A child born abroad (out of wedlock) to a US citizen father is a US citizen, but there are a bunch of requirements to check off.

https://travel.state.gov/content/travel/en/legal/travel-legal-considerations/us-citizenship/Acquisition-US-Citizenship-Child-Born-Abroad.html