Based on the definition of a theocracy, such a system can not officially be found in the United States government.
The United States Constitution makes it clear that the Church and the State are different entities which means that people of all faiths can be in the government.
The reality is a little different however because there are states that are quite conservative in governance owing to the their beliefs in Christian doctrine. The arms of government of the federal government also have a lot of Christians in them. For example, the Supreme Court has a lot of Catholics as justices.
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