“As early at 1350, the British Parliament approved statutes recognizing the rule of jus sanguinis, under which citizens may pass their citizenship by descent to their children at birth, regardless of place. Similarly, in the its first naturalization statute, Congress declared that ‘the children of citizens of the United States, that may be born beyond the sea, or out of the limits of the United States, shall be considered as natural born citizens.’ 1 Stat. 104 (1790) . . . . Notwithstanding the Supreme Court’s discussion in Wong Kim Ark (1898), a majority of commentators today argue that the Presidential Eligibility Clause incorporates both the common-law and English statutory principles, and that therefore, Michigan Governor George Romney, who was born to American parents outside of the United States, was eligible to seek the Presidency in 1968."
Meese, Edward, Heritage Guide to the Constitution, p. 190 (2005).”
So yes, Senator Cruz is eligible to be President of the United States.