The Constitution of the United States of America was originally put into place to define the role of government and protect the rights of its citizens. The Bill of Rights applies to everyone in the United States, including illegal immigrants, concerning due process and the fifth and sixth amendment. . The Bill of Rights never specifies that it is for 'citizens' only or 'Americans.' Some rights do not extend to immigrants, legal or illegal, like the right to vote or hold office.
Torture would definitely violate the Eighth Amendment for U.S. citizens, falling into the domain of "Cruel and Unusual Punishment," and the victim would be able to file suit against the perpetrators.
The shady area of this question is if non-citizens, for example suspected terrorists, are being tortured, they would have an extremely difficult time protesting their mistreatment, especially if the torture happened off US soil.
The enotes link below has some really great reference to court cases involving the Eighth Amendment.