Carmichael John Williamson, known as John, denied three charges of rape and a further charge of underage sex but was convicted following a trial at the High Court in Edinburgh.
The crimes took place in the Shetland area, police said.
Judge John Morris KC described the case as “very distressing” and told jurors that counselling was available should they require it.
Williamson, of Burra, was placed on the sex offenders’ register and remanded in custody ahead of his sentencing on 8 December.
The rapist, who the court heard has served as a police constable for more than 10 years, was visibly upset as he was led from the dock in handcuffs.
Williamson, 32, was convicted of having underage sex with a 15-year-old girl on various occasions between April and September 2014 and raping her on one occasion between April 2014 and October 2015.
He was additionally found guilty of raping a woman in 2020 and again in 2022 while she was intoxicated and incapable of giving consent.
Police Scotland said Williamson was arrested, charged, and suspended from duty on 10 January 2024.
Detective Superintendent Stevie Bertram, of Police Scotland’s public protection unit, said: “Reports of violence against women and girls are rising and it is of the utmost importance for Police Scotland to play its part in tackling this national emergency.
“Our thoughts are very much with the victims in this case, and I wholeheartedly commend their strength in reporting these crimes.
“This was the crucial first step in bringing Williamson to justice.
“Williamson will now face the consequences of his actions and today’s outcome should highlight our determination to relentlessly pursue the perpetrators in these investigations.
“I hope that this outcome may bring some closure to those affected by this case.”
The force said Williamson was a special constable at the time of the offences in 2014-2015, and was a serving officer during the 2020 and 2022 attacks.
DS Bertram continued: “We understand how difficult it can be to report these kinds of offences, particularly when the perpetrator is a police officer.
“I want to reassure the public we will identify and investigate these officers whether they are serving or retired, or whether their crimes are committed on-duty or, as in this instance, off-duty.
“We are absolutely committed to rooting individuals who are involved in criminality out of this organisation.”
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