Most Christians are conservative, but most conservatives are not Christians.
However, back when this country was founded, and our Government emblazoned all of our money with the significant slogan "In God We Trust", (not "Bhudda" or "Allah" or "Krishna", but GOD) and decided that all Americans should swear to an oath on a Bible, whether in Court or in an official ceremony...
...yes, Conservatives were Christians. As were most Americans.
In fact, most of the original States in the Union had official State Churches! Now that's true conservatism, BABY!