America’s unofficial arbitrator-in-chief has a new job — advising General Motors Co. on how to handle the ignition-switch defect linked to at least 13 deaths.

While testifying before Congress on Tuesday, GM Chief Executive Mary Barra disclosed that the company had hired Kenneth Feinberg, reports WSJ’s Neal E. Boudette. While Ms. Barra didn’t say the company would set up a compensation fund for victims, bringing on board Mr. Feinberg is a strong sign that one may be in the works.

The 68-year-old Massachusetts-native has spent a career grappling with who is owed what in the aftermath of what seems like every major tragedy and crisis to strike America in recent years. A Yale business professor once dubbed him a “modern-day King Solomon.”

After the 2010 BP oil spill, he was tapped to manage the company’s $20 billion damage fund. Before leaving the post in 2012, he handed out $6.1 billion to more than 200,000 individuals and businesses.

Before that, he served as the Obama administration’s “pay-czar”, a job created by the 2009 stimulus law to oversee executive compensation practices at financial firms bailed out during the financial crisis.

He’s administered or...