Sotomayor made what appears to be her first public decision as a justice on Monday, voting unsuccessfully to delay the execution of an Ohio death row inmate.
She voted along with the court's liberal bloc - Justices John Paul Stevens, Ruth Bader Ginsburg and Stephen Breyer - to stop the execution of Jason Getsy, whose execution is Tuesday.
Getsy had asked the nation's high court Monday to allow him to challenge Ohio's lethal injection system as cruel and unusual punishment. The court's other five justices voted to deny the stay.
Getsy, 33, was sentenced to die for shooting 66-year-old Ann Serafino in 1995 in Hubbard, Ohio, near Youngstown.
The Supreme Court said Sotomayor did not participate in the court's other death penalty decision of the day: to order an evidentiary hearing for death row inmate Troy Davis, whose lawyers say they have evidence that he did not kill the off-duty police office for which he was condemned.
Sotomayor, 55, became the first Hispanic and third female justice in the court's 220-year history after taking an oath of office earlier this month from Chief Justice John Roberts.
She will sit in on her first Supreme Court hearing on a key campaign-finance case on Sept. 9. The new term doesn't formally kick off until Oct. 5.