I saw this in an article from the Micah Challenge that got it from the Mennonite's magazine.
This is a small excerpt but says why I think we should vote:
We are citizens of our communities—many of us leaders, and we take advantage of much that our communities offer. We can’t just refuse to help set the direction of our towns and counties and nation!
Besides, if we believe that God instituted government for the good of people, and we live in a democracy where we are the government, isn’t it our duty to help our government do the things God instituted it to do? We Christians can do a lot, through the government as well as outside it, to improve the condition of our fellowman, to promote Christian order and justice and the reign of peace. Goodness, with all the drunkenness in our land, we certainly can vote to promote more Christian behavior.
-Anna Landis Funk (from two letters written by her in 1880 in Indiana)
You can read the whole thing here.