Birthright is the concept of things being due to a person upon or by fact of their birth, or due to the order of their birth. These may include rights of citizenship based on the place where the person was born or the citizenship of their parents, and inheritance rights to property owned by parents or others.
Ted Cruz is a good example of your case and explains how he could run for president under current laws.
Rafael Edward Cruz was born on December 22, 1970,[2][3] at Foothills Medical Centre[4][5] in Calgary, Canada, to Eleanor Elizabeth (née Darragh) Wilson and Rafael Cruz.[6][7][8][9] Eleanor Wilson was born in Wilmington, Delaware. She is of three-quarters Irish and one-quarter Italian descent, and earned an undergraduate degree in mathematics from Rice University in the 1950s.[10][11]