There are essentially five words with "цы" in the root: цыган, цыпочки, цыплёнок, цыкнуть, цыц. It seems to be a norm in endings and suffixes (лисицын, куцый) while "и" is an exception. I think the letter is used only in words with "-ция": полиция, акция. I am not sure whether "ций" is part of roots in words like "кальций", "стронций".
P.S. Pronunciation doesn't depend on the spelling in this case.