Can Mormon women be ordained priests in the LDS Church?

No.  In the LDS Church only men are given the priesthood and ordained to ecclesiastical office.  Various explanations have been offered over the years to explain this state of affairs.  Most commonly, it is explained that women are given the gift of motherhood and men are given the priesthood.  There is however, no “official” position on the matter.

Indeed, this issue has been a source of contention between the institutional church and Mormon feminists who claim a right to hold and exercise priesthood authority.  It is true that in the 19th century it was common for Mormon women to lay on hands, giving blessings to each other and also to their children and that this practice was phased out by Church leadership.  Michael Quinn argues that women hold priesthood once they have been through the LDS endowment ceremony and have done so since 1843.

Today, women perform priesthood ordinances in LDS temples under the direction of the Temple’s (male) president.

There is no canonical injunction (explicit or otherwise) against women holding priesthood authority in LDS scripture.  Indeed, the OT offers several examples of women such as Deborah and Huldah who are called prophetesses and seemingly command the ecclesiastical respect of their peers.  Thus, it is conceivable that the LDS Church could extend priesthood office to women and be on safe scriptural ground.  However, such an action would require a new revelation and, at least to this author seems very unlikely.

Additionally, most Mormon women seem completely comfortable with current church practices and those who advocate for change seem to be in the minority. Mormonism, like Catholocism is quite conservative and its adherents are generally respectful of long-standing church policies and practices.

Mormonism tends to support conceptions of the nuclear family and in general, discourages women from working outside the home when children are present.