In order for a male to be entered into the covenant of Abraham, it is not enough for him not to have a foreskin. Rather, a circumcision needs to be carried out by a G‑d-fearing Jew, with the express intention to perform the mitzvah of brit milah.

So what is done for someone who was born without a foreskin or was circumcised by a doctor? Assuming that the lack of foreskin meets the standards of halachah, the solution is a simple and painless procedure, known as hatafat dam brit, by which a drop of blood is symbolically drawn from the circumcision area.

Today, this is generally done with a sterile needle and is quick and with no before- or after-care. While it is not accompanied by the blessings and prayers that are said during a full-blown circumcision, it is customary to celebrate with a feast.


Sources:
Talmud, Shabbat 134b ff.; Code of Jewish Law, Yoreh Deah 265:3.