If you vote, you can have a say.
Or you'd also have to put a comma after any other dependent clause beginning a sentence. So we should put a comma after dependent clause—why?
It is not required to put a comma after a dependent clause, and some writers don't. Here are two examples from journalists writing in today's Guardian newspaper:
Unless the public gets angry enough to force a rethink we had better hope that at least the computer stays risk-averse.
Every time a "periodic" falls off the wagon they hit the ground harder.
Nevertheless, except in the case of very short dependent clauses, it is generally courteous to the reader to insert a comma, since it makes the sentence easier to parse. In some cases omitting the comma will result in a momentary ambiguity:
While I was cooking my daughter did her homework.
If you do so, it will be because it marks a prosodic break in the sentence: If you vote and you can have a say are separate breath groups. There may or may not be an audible pause between them, but there will almost certainly not be a pause elsewhere and no pause between vote and you.
There's no why for everything in languages. A comma is more like a short pause between clauses, words and phrases. In the case you mentioned, the comma would make it clearer and easier to read. If you don't care about the clarity of your sentence, you can drop the comma and it would still be fine– just a little harder to read.