A convert's biological parents are not their parents in a halachic sense. In some senses the converting beis din is "responsible" for the convert in the way of parents. In name, at least, the ger's parents are Avrohom Avinu and Sarah Imenu. When, if ever, does a convert say yizkor?
As a convert, I've only asked the question with respect to kaddish and shiva. I've posted the answers I've received on those questions elsewhere (in sum, my rav relying on the Rema said "no kaddish or shiva" but there are other chashuva sources who disagree; I go with my Rav). Since my late Rav, Rabbi Gedaliah Anemer, zt'l, said "no" to those questions, it never occurred to me to ask about Yizkor. But I do know that with respect to my Jewish-born wife, Rabbi Anemer (and his student and successor, Rabbi Dovid Rosenbaum, shlita), said she could not say Yizkor until her parent had been dead one year. Given that I never bothered asking about Yizkor. I don't know any converts who stay around for Yizkor, and I don't either.
A convert should not say Yizkor for his\her non-Jewish parents, for the simple reason that the text of Yizkor is specific to Jews (as we ask God to bind the soul of the deceased with those of their ancestors Abraham, Isaac, Jacob, Sarah, Rebecca, Rachel and Leah.)
However, a convert may say a personal prayer in remembrance of his\her parents in place of the traditional Yizkor prayer.
For practical applications, please consult your rabbi.