[paltz]

Sure it isn't:

https://www.uscis.gov/us-citizenship/citizenship-through-naturalization

"Naturalization is the process by which U.S. citizenship is granted to a foreign citizen or national after he or she fulfills the requirements established by Congress in the Immigration and Nationality Act (INA)."

[Ray76]

I suggest you read Rogers v. Bellei

[Ray76]

A person born out of the jurisdiction of the United States can only become a citizen by being naturalized

either by 

    treaty, as in the case of the annexation of foreign territory, 

or by 

    authority of congress, exercised 
	
    either by 
	
        declaring certain classes of persons to be citizens, as in the enactments conferring citizenship upon foreign-born children of citizens, 
	
    or by 

        enabling foreigners individually to become citizens by proceedings in the judicial tribunals, as in the ordinary provisions of the naturalization acts.

U.S. v. Wong Kim Ark, 169 U.S. 649, 702-703

[Ray76]

The minor children of aliens naturalize upon the naturalization of their parents. The child does not participate in any process yet they are naturalized.

[Cboldt]

-- "Naturalization is the process by which U.S. citizenship is granted to a foreign citizen or national after he or she fulfills the requirements established by Congress in the Immigration and Nationality Act (INA)." --

From 7 FAM 1441.1 (State Department Manual), the process is the following:

f. The Form FS-240 is not a birth certificate, such as is issued by a government- authorized bureau or office of vital statistics, because consular officers are not authorized to assume a foreign local or state vital statistics function. The Form FS-240 is a consular declaration of the fact of acquisition of U.S. citizenship at birth based upon:

(1) The certification of, or attestation to, the facts of birth by a legally authorized local official in the place where the birth occurred;

(2) The affidavit executed by the parent(s) or legal guardian(s) or other evidence regarding the physical presence of the U.S. citizen/national parent(s), or in the case of two citizen parents, residence, necessary to transmit U.S. citizenship/noncitizen nationality to the child;

(3) Evidence of the physical relationship between the U.S. citizen and the child;

(4) Evidence of the legal relationship between the U.S. citizen and the child, such as proof of the U.S. citizen/national parent(s)'s citizenship and marriage or for births out of wedlock, legitimation in accordance with Section 309 INA (8 U.S.C. 1409) or predecessor statute, and an affidavit of parentage and financial support if the child is born out of wedlock to a U.S. citizen father;

(5) Evidence of citizenship/nationality of the U.S. citizen/national parent(s); and

(6) Consular adjudication of the child's claim to U.S. citizenship. (See 7 FAM 1100.)

This process need not be done by the State Department. It can also be done by USCIS (Immigration and Naturalization), or by an Article III Court.