No. Everyone needs to have a voice in a democracy. Would those who were not allowed to vote still have the "privilege" of paying income tax, sales tax, property tax, tobacco and alcohol taxes? Because if you create a voting and non-voting class, the voters could vote to tax the crap out of the non-voters. And that's just the tip of the iceberg. If you can vote and I can't, you could vote to close the public school that my kids go to. Maybe whoever invented the test thinks I'm not smart enough to vote, but don't I have a right to try and make things better for my kids so that they'll be smarter than me?
And who would come up with the criteria for this test? I could see that becoming very partisan. Someone on the test development committee might decide that if you profess a belief in Creationism that you can't vote, or atheists might decide that if you believe in a Supreme Being who created the universe that you're too stupid to vote, or Christians might decide that atheists are too stupid to vote, or your opinion on abortion, capital punishment, or any number of other controversial topics might become a litmus test for your voting rights.
And above all, if a person is to be bound by the laws of a government, should not he/she have a voice in that government?
If there should be a test for anything, it should be a test for whether or not you qualify to hold public office. If a politician can't win on the game show, Are You Smarter Than a Fifth Grader? he/she should not be allowed to run for Congress or the Presidency.