Naude, 30, was a Police Constable with Cheshire Constabulary, near Manchester, when he attacked the girl, who he had met when he was investigating a domestic incident.
On Thursday, December 13, Judge Clement Goldstone QC said Naude was "out of control" and had an "insatiable appetite" for young girls.
Judge Goldstone referred to a selfie Naude took in his car after raping the girl as being full of "smug self-satisfaction and a total lack of shame".
Naude had denied rape — forcing the girl to go through her ordeal in court — and claimed it was consensual sex and she "seemed to be enjoying it".
A policeman has been jailed for a string of sexual offences against young girls including raping a 13-year-old girl in his car and filming it. Constable Ian Naude, 30, was jailed for 25 years. The jury was told he joined the police to meet vulnerable young girls @cheshirepolice pic.twitter.com/RvlTXzdwZM— Amanda Nunn (@amandaDnunn) 13 December 2018
Naude, who had moved to Britain from South Africa, was also convicted of four charges of attempting to arrange the commission of a child sex offence and one charge of arranging a child sex offence, relating to five complainants aged between 12 and 15.
He has previously admitted 31 offences including charges related to grooming under-age girls via a fake Facebook and Snapchat profile.
The trial at Liverpool Crown Court heard he contacted the girl over social media and arranged to meet her.
Filled With 'Lust and Perversion'
"In order to impose your will on a young girl and to commit offences of rape and sexual assault against her, you used and abused your position as a Cheshire Police officer, thereby enabling you to satisfy your lust and perversion," Judge Goldstone told him.
Detective Inspector Kate Tomlinson, the senior investigating officer for this case, said Naude was a "sexual predator of the most evil kind."
"He joined Cheshire Police with the sole purpose of gaining a position of trust so he could prey on young, vulnerable girls," said Det. Insp. Tomlinson.
"It was Ian Naude's job to enforce the law and protect people from harm. Instead he became the most dangerous of predators and betrayed the very people he swore to protect," added Det. Insp. Tomlinson, who praised the "incredible bravery" of Naude's victims.