"唱弥撒的神父" can be translated as "the priest celebrating Mass" or "the priest who sings/conducts the Mass".
In a religious context, "celebrating Mass" is a common and accurate way to describe a priest performing the Eucharistic service (弥撒). If you specifically want to emphasize the act of singing during the Mass, you could use "the priest who sings/conducts the Mass," though "celebrating Mass" already encompasses the entire liturgical action, which typically includes singing.