Google Translate comes up with the phrase, Es ist dein Umzug, but I have a feeling that "Umzug" is the wrong word here. I think that "Zug" would be more appropriate.
The reason for this intuition is simply that "zug" is already found in a number of chess terms, e.g. "zwischenzug" for "in-between move" and "Zugzwang" for "compulsion to move".
Thus, I would be tempted to say Es ist dein Zug or dein Zug for short. Is my intuition correct?