From Clergy | oca.org (Orthodox Church in America), the rector is appointed by the Diocesan Bishop and cannot leave his parish without the permission of the Bishop.
Below is the entire section:
At the head of the parish is its Rector. According to the teachings of
the Church, he is the spiritual father and teacher of his flock and
the celebrant of the liturgical worship established by the Church. He
teaches and edifies the People of God entrusted to his spiritual care
"with no partiality" (James 2:1) and sees to it that all activities
within the parish serve the religious goals of the Church.
The rector is appointed by the Diocesan Bishop and cannot leave his
parish without the permission of the Bishop. No activities in the
parish can be initiated without his knowledge, approval, and blessing;
neither should he do anything pertaining to the parish without the
knowledge of his parishioners and parish organs elected by them, so
that always and everywhere there may be unity, mutual trust,
cooperation, and love. In conformity with his teaching office, the
Rector shall have final authority over the church school. To be free
from material preoccupations and wholly committed to his sacred
ministry, the priest must be compensated by the parish, the amount of
his compensation being clearly agreed upon at the time of his
See also: Article X: The Parish | The Statute of the Orthodox Church in America.
Answering Say for instance, his wife had strong family ties in a certain state. Could he request assignment in a certain state? How likely is that request to be granted?
I would say first step is for the rector to speak with his Bishop.