While historically anarchists assiduously avoided any involvement with electoral politics, in more recent times, at least in the united states, some anarchists have advocated voting. The arguments these voting anarchists put forward are generally the same as those put forward by other leftists who are unable or unwilling to completely sever their connection to the political process. The primary reason why anti-statists should not vote, and in fact should oppose voting, is that the very act of voting is an attempt on the part of voters to delegate to another a power that they could not justly possess themselves.
Government is based on coercion.
While states of various sorts provide some services and benefits to residents of their jurisdictions, the institution of government also utilizes cops, courts, the military, the IRS, etc, to coercively interfere in the lives of its subjects. Anarchists argue that no one, whether in or out of government should have such power. If this is true, anarchists, who oppose political power and coercion of any sort, cannot consistently advocate voting. Individuals should not have the authority to coerce others, and therefore they should not put themselves in a position to delegate such authority to third parties, which is the essence of voting. Besides being unethical for an anti-authoritarian in and of itself, participation in electoral politics serves to legitimize the whole political process and the existence of government.