The question was posed, “Where in the Bible does it talk about voting?” The Bible does not specifically mention “voting.” The New Testament, though, does teach that mankind is obligated to obey civil government.
Let every soul be subject unto the higher powers. For there is no power but of God: the powers that be are ordained of God. Whosoever therefore resisteth the power, resisteth the ordinance of God: and they that resist shall receive to themselves damnation. For rulers are not a terror to good works, but to the evil. Wilt thou then not be afraid of the power? do that which is good, and thou shalt have praise of the same: For he is the minister of God to thee for good. But if thou do that which is evil, be afraid; for he beareth not the sword in vain: for he is the minister of God, a revenger to execute wrath upon him that doeth evil. Wherefore ye must needs be subject, not only for wrath, but also for conscience sake. For for this cause pay ye tribute also: for they are God’s ministers, attending continually upon this very thing. Render therefore to all their dues: tribute to whom tribute is due; custom to whom custom; fear to whom fear; honour to whom honour. (Romans 13:1-7).
God has not ordained any particular form of civil government (e.g., monarchy, democracy); however, God nevertheless sanctions civil government. The government dominating the first century civilization ringing the Mediterranean Sea was the harsh Roman Empire. Further, 1 Peter 2:17 says, in part, that mankind is obligated to “…honor the king.”
In democratic forms of government, citizens participate in government by voting for candidates who will represent them or by voting for or against referendums. Both Romans 13:1-7 and 1 Peter 2:17 portray inspired penman instructing Christians to appropriately respond toward the government under which they live. Hence, people living under democratic governments ordinarily participate by casting their votes.
In the past, especially in southern states in America following the Civil War, some Christians (e.g., David Lipscomb) refused to cast votes and chose to have as little to do with government as possible. Lipscomb wrote about civil government and attempted to portray any degree of participation in government by Christians as improper. His view did not widely prevail and to my knowledge no one today (i.e., in the churches of Christ) understands Scripture to so teach. One or more other religious groups, though, abstain from virtually every association with government, including voting.
Noting biblical references to the Christian’s obligation to acknowledge government and comply with it (as long as it does not demand direct violation of God’s Word, Acts 5:29), one will have to exercise his personal judgment as to whether he will cast his vote under a democratic form of government. Voting for candidates, for instance, who uphold biblically moral issues that also happen to be political issues is one way in which one can both respond to government and attempt to promote God’s will in society.