Maryland court records show that on Jan. 29, 2018, the U.S. government obtained a lien against Moore in the amount of $75,328.80.
The lien is for unpaid income taxes and related penalties and interest from the 2014 filing year. The lien was filed in Circuit Court in Montgomery County. Moore lives in Potomac, Maryland, which is located in that county.
President Donald Trump said last week that he intends to nominate Moore for a Fed governorship.
Moore did not immediately respond to a request for comment from CNBC.
Moore believes the central bank should cut interest rates by half a percentage point, a position well out of line with other policymakers.
In an interview with the New York Times on Tuesday, the Heritage Foundation fellow and former Wall Street Journal editorial board member backed off earlier criticism he had for the Fed and specifically its chairman, Jerome Powell.
Shortly after the Fed enacted its fourth rate hike of 2018 in December, Moore wrote in a Heritage blog post entitled "Fire the Fed" that Powell should "do the honorable thing ... and resign."
The lien was first reported by The Guardian.
—CNBC's Jeff Cox contributed to this report