The fiend busted for raping a New Jersey jogger before drowning her in a lake is an illegal immigrant from Honduras who had already been kicked out of the US twice before, authorities said Thursday.

Jorge Rios, 33, was deported from the US first in 2003 and then again in 2004, but snuck back across the border at some point after that, they said.

Surveillance video showed that Rios stalked Carolina Cano, 45, before he strangled her with a cellphone cord, raped and drowned her as she was out for an early morning jog in Jersey City’s Lincoln Park on March 24, authorities said.

And immediately after the heinous crime, he strolled over to a friend’s place — and asked him how much time he could get for murder.

Cano, a native of Peru who lived nearby, died “as a result of homicidal violence including strangulation and water submersion,” according to a criminal complaint against Rios obtained Thursday by The Post. And cops said he confessed during questioning.

The court papers painted a nightmarish picture of Cano’s last moments as her alleged killer ruthlessly hunted her down at least an hour before the 6:26 a.m. sunrise that Sunday morning.

Video showed that Rios skulked into the park at about 5:10 a.m. and was seen “milling around” the south side of the lake — the area where Cano’s body would later be found floating by Hudson County Sheriff’s officers, the court papers said.

Surveillance video then showed Rios walk back up to Lakeview Drive, where the unsuspecting Cano jogged past him.

“The male observes the victim and proceeds to walk behind her. Upon approaching the football parking lot, the victim is seen running with the male running directly behind her,” an affidavit for Rio’s arrest said.

“The male is seen continuing south, stopping, turning to look behind him towards the victim, and then running in the same direction as the victim.”

The document said that Rios could be seen on the surveillance footage leaving the park at 6:17 a.m. and walking toward a friend’s house nearby.

“How much time do you think a person would get for killing someone,” he asked his pal, according to the documents.

Rios, of Jersey City, was charged with murder, kidnapping and aggravated sexual assault, according to the prosecutor’s office.

He was taken to Hudson County Correctional Facility after his arrest and remanded.

Rios — whose full name is Jorge Alberto Rios-Doblado — was deported back to Honduras twice for entering the country illegally near Laredo, Texas, according to an ICE Newark statement.

It was unclear when and how he got back into the US the last time.

ICE put a detainer on Rios, who had no prior criminal record, cops said, and he will be deported yet again.

But if he is convicted, he will have to serve his sentence before he can be given the boot, and murder carries a possible sentence of up to life behind bars.