The Catechism of the Catholic Church is clear in its teaching that Catholics have a moral obligation to vote.
When Catholics have the opportunity to vote, the Church firmly believes that there exists a “moral obligation” to participate in an election.
This teaching is explained in the Catechism of the Catholic Church.
Submission to authority and co-responsibility for the common good make it morally obligatory to pay taxes, to exercise the right to vote, and to defend one’s country:CCC 2240
Furthermore, citizens are obligated to contribute to the common good of society.
It is the duty of citizens to contribute along with the civil authorities to the good of society in a spirit of truth, justice, solidarity, and freedom. The love and service of one’s country follow from the duty of gratitude and belong to the order of charity. Submission to legitimate authorities and service of the common good require citizens to fulfill their roles in the life of the political community.CCC 2239
At the same time, citizens must follow God above all, and not place human standards above those instituted by God.
The citizen is obliged in conscience not to follow the directives of civil authorities when they are contrary to the demands of the moral order, to the fundamental rights of persons or the teachings of the Gospel. Refusing obedience to civil authorities, when their demands are contrary to those of an upright conscience, finds its justification in the distinction between serving God and serving the political community. “Render therefore to Caesar the things that are Caesar’s, and to God the things that are God’s.” “We must obey God rather than men.”CCC 2242
The Catechism does not tell us “how” to vote, but it does instruct us that we must vote, participating in any election that is being held in our country.