Civil lawsuits seeking damages for torture or similar grave misconduct by corporations outside the United States are often brought under the U.S. Alien Tort Claims Act (a.k.a. ATS) in U.S. federal courts. Multiple cases brought under the Alien Tort Claims Act have involved claims that U.S. corporations, through their agents carrying out company policy, tortured people outside the U.S., or were complicit in conduct that caused someone to be tortured by a government.
One example is the case of Wang Xiaoning v. Yahoo!
In 2007, the World Organization for Human Rights USA filed a lawsuit
against Yahoo! on behalf of Chinese dissidents Wang Xiaoning and Shi
Tao (Guao Quingsheng), claiming jurisdiction under the ATS. According
to the complaint, Wang and Shi Tao used Yahoo! accounts to share
pro-democracy material, and a Chinese subsidiary of Yahoo! gave the
Chinese government identifying information that allowed authorities to
identify and arrest them. The Complaint alleges that the plaintiffs
were subjected to "torture, cruel, inhuman, or other degrading
treatment or punishment, arbitrary arrest and prolonged detention, and
Yahoo! settled the case in November 2007 for an undisclosed amount of
money, and it agreed to cover the plaintiff's legal costs as a part of
the settlement. In a statement released after the settlement was made
public, Yahoo! said that it would "provide 'financial, humanitarian
and legal support to these families' and create a separate
'humanitarian relief fund' for other dissidents and their families."
Corporations can also be prosecuted criminally for crimes.
Pacific Gas & Electric was recently convicted of manslaughter in a California State Court related to deaths caused by wildfires that were caused by reckless disregard to maintenance and safety by the corporation. The fines were largely waived in subsequent bankruptcy proceedings with the permission of the prosecution, in order to free up funds to pay compensatory damages to parties prevailing in civil lawsuits and funds to comply with orders from utility industry regulators in the state.
Arthur Anderson, then one of the "Big Six" accounting firms in the United States was convicted of fraud related criminal charges in relation to the collapse of Enron, an oil company for which it was an accountant, that resulted in the demise of the firm, even though the conviction was ultimately reversed on appeal by the U.S. Supreme Court.
I am not aware of a case in which a U.S. corporation has been prosecuted criminally for authorizing its agents to torture someone or being complicit in torture, but it certainly could be done (and probably has been done).
The federal Racketeering and Corrupt Organizations Act (RICO) and parallel state statutes, are specifically designed to authorize both criminal and civil actions against corporation or de facto entities engaged in criminal activity. The statute was designed to target organized crime activities, particularly those involving corporations used as fronts for criminal activity, and in the criminal context, the focus of prosecutions has largely continued to be on old school mafia type organized crime gangs and cartels. But private civil actions authorized by RICO against companies engaged in a pattern of criminal activity usually involve allegations of a pattern of fraud and other forms of white collar crime. This would be a likely statute to invoke in a criminal case alleging that a company had engaged in a pattern and practice of torturing people.
In practice, the difference between a civil lawsuit in which compensatory and punitive damages may be imposed, and a criminal prosecution of a corporation, in which fines and restitution may be imposed, is subtle indeed when it comes to the remedies available in each case, even though procedurally, the two kinds of legal proceedings are very different, which is why usually a civil lawsuit, rather than a criminal conviction, would be the legal tool of choice when a corporation engaged in conduct, through its agents, which is criminal in nature.
Also, it is possible, but harder, to prosecute officers, employees and agents of corporations in addition to the corporations themselves, for criminal conduct. Indeed, this is the usual approach. But it is harder to convict an individual because you have to show that the individual had the requisite intent and was personally involved in the criminal conduct. This typically requires access to internal communications in a firm which can be difficult to obtain in a criminal proceeding that doesn't have as much pre-trial discovery, and can be difficult to establish because responsibility within a large corporation is often diffuse.
Generally speaking, prosecutors have seen the Arthur Anderson case as an unjust one and a cautionary tale that encourages them to think twice before prosecuting a major U.S. corporation criminally, rather than merely bringing a civil lawsuit against it.