Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is Mine; I will repay, saith the Lord. (Romans 12:19, quoting Deuteronomy 32:35)
The purpose of the State is to take vengeance. It was invented by those who would not wait for the Lord to repay. If it is sinful for me to take vengeance, it is sinful for me to hire someone to take vengeance for me (a mafia hit-man), and it is sinful for me to "vote" for someone to take vengeance for me. The State is therefore precluded by this passage.
John Calvin's comments on this passage are found here.
Even if the State were a completely voluntary association, which did not finance its activities by initiating force or threats of force against others in order to confiscate their wealth, its fundamental purpose -- taking vengeance -- is sinful and prohibited to all human beings.
The Biblical Prohibition of Vengeance
Vengeance belongs to God; He will repay
Ludwig von Mises on the Vengeful State