The Bible says we should do everything we possibly can to be good citizens and work for the betterment of our society, and one of the ways we can do this is by voting. God tells us to "seek the peace and prosperity of the city to which I have carried you" (Jeremiah 29:7).
Rightly or wrongly, you say you're disillusioned by what you see in politics today. But how will it be changed? Let me tell you how it won't be changed: It won't be changed if concerned people refuse to vote! It also won't be changed if good people refuse to run for office, or if no one votes for them. In other words, staying away from the voting booth may only perpetuate the problems you see. Although this election has passed, don't let another one go by without your intelligent involvement.
Christians in the first century didn't have the privilege of voting; Caesar was a dictator, not elected by popular vote. But those early believers were commanded to do the one thing they could do to make the world a better place: They were told to pray. The Apostle Paul wrote, "I urge, then, first of all, that petitions, prayers, intercession and thanksgiving be made for all people -- for kings and all those in authority" (1 Timothy 2:1-2).
Our world will never be perfect -- not until Christ returns. But in the meantime, God wants to use us to overcome sin and establish a more just world for His glory.