I was born abroad. My American mother was married to my Spanish father when I was born. Do I have a claim to US citizenship?

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