Any person, including a minor, can renounce their US citizenship when expatriate themselves.
7 FAM EXHIBIT 1292
A SAMPLE LETTER TO ACCOMPANY CLN FOR MINOR RENUNCIANTS
Post Letterhead Date
Dear (Name):
Every U.S. Citizen has the right to renounce voluntarily and intentionally his or her citizenship, as you have done. Because this is a very serious decision with consequences that may not have been apparent to you at the time, the law gives persons like yourself who renounced under the age of 18 an opportunity to reevaluate your decision when you reach the age of 18.
Section 351(b) of the Immigration and Nationality Act (8 U.S. Code 1483) allows you to reclaim your U.S. citizenship within 6 months ...
The rest of the sample letter can reviewed on the internet after a simple search.
Barry Soetoro recieved such a letter and would not have been allowed to become an Indonesian National if he had not received his CLN from the US.