So far as I know, he wasn't, just placed under house arrest.

According to Owen Gingerich's The Great Copernicus Chase, the 1633 decree calling Galileo to be interrogated* read, in part, as follows:

Galileo Galilei ... is to be interrogated concerning the accusation, even threatened with torture, and if he sustains it, proceeding to an abjuration of the vehement [suspicion of heresy] before the full Congregation of the Holy Office, sentenced to imprisonment....

(Emphasis added.) Gingerich goes on to say:

On the next page the results of the interrogation are recorded. In Italian are Galileo's words: 'I do not hold and have not held this opinion of Copernicus since the command was intimated to me that I must abandon it.' Then he was again told to speak the truth under the threat of torture. He responded: 'I am here to submit, and I have not held this opinion since the decision was pronounced, as I have stated.' Finally, there is a notation that nothing further could be done, and this time the document is properly signed in Galileo's hand. Galileo was sent back to his house at Arcetri, outside Florence, where he remained under house arrest until his death in 1642.

(Emphasis added.) These quotes can be seen using Amazon's "Look Inside" feature. This link worked for me. These passages are also excerpted in this pdf.

So, Galileo was explicitly threatened with torture, though he was not actually tortured and may not even have been "shown the instruments of torture" (which is the strongest claim made in reputable sources). As I argue in this thread, I believe that this justifies saying that the Church used torture (as an institutionalized practice) to force Galileo to recant.

* An earlier version of this comment referred here to "the 1633 sentence entered against Galileo" because I misread Gingerich's use of the word "sentence" to refer to a sentence of punishment, but he just meant a grammatical sentence ><.

The modern conception of Galileo as someone harshly prosecuted for his beliefs seems rather exaggarated: in reality, he was even explicitly encouraged to write a book on the subject by the church. It was only when he offended the Pope in his book that he got sent to house arrest.

In the end, Cardinal Bellarmine, acting on directives from the Inquisition, delivered him an order not to "hold or defend" the idea that the Earth moves and the Sun stands still at the centre. The decree did not prevent Galileo from discussing heliocentrism hypothesis (thus maintaining a facade of separation between science and that church). For the next several years Galileo stayed well away from the controversy. He revived his project of writing a book on the subject, encouraged by the election of Cardinal Maffeo Barberini as Pope Urban VIII in 1623. Barberini was a friend and admirer of Galileo, and had opposed the condemnation of Galileo in 1616. The book, Dialogue Concerning the Two Chief World Systems, was published in 1632, with formal authorization from the Inquisition and papal permission. [...]

Earlier, Pope Urban VIII had personally asked Galileo to give arguments for and against heliocentrism in the book, and to be careful not to advocate heliocentrism. He made another request, that his own views on the matter be included in Galileo's book. Only the latter of those requests was fulfilled by Galileo. Whether unknowingly or deliberately, Simplicio, the defender of the Aristotelian Geocentric view in Dialogue Concerning the Two Chief World Systems, was often caught in his own errors and sometimes came across as a fool. Indeed, although Galileo states in the preface of his book that the character is named after a famous Aristotelian philosopher (Simplicius in Latin, Simplicio in Italian), the name "Simplicio" in Italian also has the connotation of "simpleton."[48] This portrayal of Simplicio made Dialogue Concerning the Two Chief World Systems appear as an advocacy book: an attack on Aristotelian geocentrism and defence of the Copernican theory. Unfortunately for his relationship with the Pope, Galileo put the words of Urban VIII into the mouth of Simplicio. Most historians agree Galileo did not act out of malice and felt blindsided by the reaction to his book.[49] However, the Pope did not take the suspected public ridicule lightly, nor the Copernican advocacy. Galileo had alienated one of his biggest and most powerful supporters, the Pope, and was called to Rome to defend his writings.

I got burned during a debate because I trusted the history from my physics textbook. After having read several books on the history of science (rather than summaries inside larger works) I am convinced that the Dark Arts on on full display even in natural science coursework.

"Torture" here is analogous to "shooting", not "crime".