The NYPD has gotten a DNA profile from the fedora worn by the sadistic predator who raped a missionary inside NYU’s Catholic Center early this month, The Post has learned.

Investigators “put a rush” on testing the profile against those in the CODIS system, law enforcement sources said.

The Combined DNA Index System operates national databases of DNA profiles from convicted offenders, unsolved crime scene evidence and missing persons.

“If we get a hit, then it’s a very good chance that it’s the guy,” said one source. He was wearing the hat during the rape. The victim confirmed it.”

The 24-year-old missionary, who’s also a student at the University of Illinois, was opening up the Catholic Center to make breakfast for the homeless at 5:30 a.m. on Nov. 1, when the sicko set upon on her, cops said.

Surveillance video later recovered by police showed the fiend stalking the woman along Sixth Avenue just minutes earlier.

The unidentified man, wearing a black fedora, dark grey sweater and dark pants, dragged her inside the center and pummeled her face, cops said.

He ordered her to “take off your shorts while choking her, a source said.

He then raped her as she recounted the “Hail Mary” prayer, the source said.

The thug then sneered, “I should have killed you,” and ran off with her tote bag and iPhone, sources said. He left behind the fedora.

The victim didn’t initially tell investigators that she was sexually assaulted, a source said.

Later on, at the hospital, she finally admitted that she was raped, the source said.