Holy Cross Orthodox Press, the publishing arm of the Holy Cross School of Theology, an institution of the Greek Orthodox Archdiocese of America, publishes the Gospel Book and the Apostolos (Book of Epistles) which use the Revised Standard Version of the Bible, if I'm not mistaken. These publications were both endorsed by Archbishop Iakovos of America, of Blessed Memory. "The Orthodox Study Bible," which is used in church too, uses the New King James Version and is endorsed by the Standing Conference of Orthodox Bishops of the Americas (SCOBA), the predecessor of the Assembly of Canonical Orthodox Bishops on North and Central America (ACOB).
None of the commonly distributed English language bibles are officially accepted for worship services primarily, because their Old Testaments do not include all the books of the Septuagint, the Apocrypha. Only the Greek language "Evangelion" ("Book of the Gospels") published by the Ecumenical Patriarchate in 1904 is officially authorized for use in the Divine Services of the churches, that are under the jurisdiction of the Church of Constantinople.
I am distinguishing herein with "officialy approved," vs. "endorsed" and "used."
The "Common Bible," which used the Revised Standard Version, published in the 1970's, included the Apocryphal books of the Septuagint and was endorsed by Archbishop Iakovos also, but for some reason was never commonly used in Orthodox Church worship.