The correct answer is C) the Legislative.
According to Article I of the U.S. Constitution, the legislative branch has the power "To establish a uniform Rule of Naturalization"
Yes, indeed, Article 1 of the United States Constitution refers to the Legislative branch in Congress with its two cameras: the House of Representants and the Senate. Article 1 grants Congress enumerated powers and the ability to create legislation and pass laws to the process mentioned here. So yes, according to Article I of the U.S. Constitution, the legislative branch has the power to "establish a uniform Rule of Naturalization"