Fethullah Gulen, who is based in the US, is accused of establishing and running an “armed terrorist group”.
He was once an ally of President Recep Tayyip Erdogan but has now been accused of plotting to overthrow the Turkish government – a claim the cleric strongly denies.
The US is thought to be unlikely to act on any extradition request.
The move comes amid a national crackdown on perceived supporters of the cleric.
Over 20 journalists working for media outlets thought to be sympathetic to the Gulen movement were arrested last weekend.
Eight of them were freed on December 19 on the orders of a court in Istanbul. Those released include Ekrem Dumanli, editor-in-chief of Zaman newspaper.
Four others, including a TV station boss, remain in custody.
While the US and Turkey have an extradition agreement, the warrant is considered to be largely symbolic – and unlikely to be acted upon.
The relationship between Washington and Ankara has grown fractious, though they remain allies.
President Recep Tayyip Erdogan has faced criticism from international leaders and his opponents, who accuse him of authoritarianism and undermining free press.
Many abroad believe that the charges against Fethullah Gulen are politically motivated.
The wealthy cleric, who operates an international network of schools and businesses, has lived in self-imposed exile in Pennsylvania since 1999.
According to media reports, the prosecutor filing the arrest warrant accused Fethullah Gulen of leading an armed terrorist group – a charge that carries up to 15 years in prison.
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