The government accuses Thaksin of spending nearly $1.5 million per day to finance the protests, and claims he helped the red shirts smuggle weapons and fighters from Cambodia.
Thaksin, who could face the death penalty if convicted of the charges, denied the charges in a series of messages posted on his Twitter page.
"As a prime minister who won two landslide election victories, I was ousted in a coup," he said.
"As I was fighting peacefully for justice for the return of my robbed assets, I was slapped with terrorism charges."
Many of the red-shirt protesters support the Puea Thai party, which is allied with Thaksin, and want early elections. They say the current government is illegitimate.
"They are saying to us, this is not the end for the former prime minister," Al Jazeera's Wayne Hay, reporting from Bangkok, said.
"This wrangling between the former prime minister and his supporters here, and the current regime, continues."
Noppadon Pattama, Thaksin's legal adviser, said he is seeking to have the warrant revoked because Thaksin's attorney was not able to present evidence in his client's defence.
In another development, opposition politicians have begun moves to impeach the Thai prime minister over his handling of the protests.
The measure, backed by 159 opposition members of parliament, not only targets Abhisit Vejjajiva, but also calls for the censure of three ministers in his cabinet: the deputy prime minister, the transport minister, and the interior minister.
The parliamentarians also tabled a no-confidence motion in Abhisit.
Neither measure is expected to pass. But the fact that they were introduced at all reflects deep rifts in Thailand's political landscape following the protests.
Wittaya Buranasiri, the opposition whip, said the impeachment motion was introduced by the Puea Thai party, whose members accuse Abhisit and his deputy of abusing their power by ordering the crackdown on the red shirts.
The red shirts have called for Abhisit to resign and allow early elections.
They accuse his government of taking power illegitimately, with the help of backroom deals and military pressure.
The anti-government movement came to a head when red-shirt protesters moved into Bangkok's central business district, building bamboo-and-tyre barricades and manning checkpoints that crippled one of the city's most important shopping and tourism areas.
Shops and businesses have begun to reopen since the crackdown, but authorities have extended a late-night curfew until next Saturday.
Abhisit's cabinet approved the extension on Tuesday.