I was born abroad. My American father was married to my German mother at the time I was born. Do I have a claim to US citizenship?

Yes, if your father was physically present in the US at least five years prior to your birth, at least two of which were after his 14th birthday (for births after 1986). Presence abroad in honorable US military service, employment with the US Government or intergovernmental international organization or as the dependent unmarried son and member of the household of a parent in such service or employment, may be included.