The United States is not a theocracy, and I for one would never want it to be a theocracy. Theocracies have proven to be very dangerous.
The United States is not secular in nature. It is supposed to be neutral. The 1787 Constitution said positive on the issue of religion vs non-religion, except that the principle was established that there would be no religious test for office. This repudiated the British policy of requiring all office holders or voters to communicate in the Church of England, which barred Catholics and Protestant dissenters as well as non-Christians. The States were left free to impose such barriers. The Bill of Rights went further in forbidding a religious establishment and passing laws that discriminated against anyone on the basis of faith. Hence the United States abandoned the idea of the Confessional State, which was the norm in Europe.