This question already has an answer here:
- Does a ger (convert) say Yizkor? 2 answers
Is a convert allowed to say Yizkor for their deceased parents if they are non-Jewish?
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.