As a Sunni woman am I allowed to get married to someone born of a Shi'a father and a Sunni mother and who considers himself to be a Sunni?
as salam alaikum
a Sunni woman can marry a Sunni man with a Shia father.
It is worth to note in this regard that three of the four major Sunni schools - the Maliki, Hanbali and Shaf'i schools - require the consent of the wali/father for marrying the woman; the Hanafi school however does not deem it necessary.
With prayers for your success.