Canon law says "clerics are forbidden to assume public offices which entail a participation in the exercise of civil power" (Canon 285.3). Furthermore, "clerics are not to have an active role in political parties and in the direction of labor unions unless the need to protect the rights of the Church to promote the common good requires it in the judgment of the competent ecclesiastical authority" (Canon 287.2). This second canon is tricky, since the "unless" opens the door to political involvement if a competent authority deems it necessary. But who might that authority be if a papal representative and national bishops' committee don't see eye to eye?
Historically, priests—including a Benedictine, a bishop, and a future cardinal—were elected to public offices before the canonical ban was set in place by Pope John Paul II in 1980. A few were elected afterward and chose laicization. Twenty-three Catholic clergy have served as ambassadors, chancellors, representatives, prime ministers, and presidents in 11 countries since the 18th century. European countries that elected or appointed priest politicians include France, Germany, Poland, Austria, Slovakia, and the Czech Republic. In the Americas, Nicaragua, Venezuela, Paraguay, the Dominican Republic, Canada, and the United States have all seen priests serving in government roles.
The first U.S. priest to serve in federal government was Sulpician missionary Gabriel Richard. Assigned to the Michigan Territory, Richard served one term as a non-voting territorial delegate to Congress. In the 1970s, Norbertine priest Robert John Cornell represented Wisconsin in Washington for two terms. Cornell withdrew a bid to regain his office in 1980 after the ban. Jesuit Robert Drinan represented Massachusetts for five terms in Congress, ending his reelection campaign after the ban.
Upon relinquishing his campaign, Cornell said, "It is my personal belief that serving in Congress is no more inconsistent with the priesthood than teaching government and history, as I have done for 35 years."
In addition, several Sisters of Mercy, a Sister of St. Joseph, and a Dominican Sister have been elected to state or city positions of governance in the United States since the ban took effect. Technically the Canon claims jurisdiction only over clergy. However, in at least three instances, the sisters in question were ordered by their local bishop to choose between politics and religious life. All three chose to retain their elected seats "to promote the common good."
Scripture: reflect on roles of biblical priest-leaders - Moses, Samuel, Ezra, Judas Maccabeus
Books: Politics in the Parish: The Political Influence of Catholic Priests, by Gregory Allen Smith (Georgetown University Press, 2008)
Catholics and Politics: The Dynamic Tension Between Faith and Power, eds. Kristin Heyer et. al. (Georgetown University Press, 2008)