It comes as the number of rapes recorded in Scotland has gone up by around one-third under the new national force, which began operations in April last year.
Nearly 1300 of the alleged crimes were recorded between April and December 2013, almost as many as in the whole of the previous year. Overall, sex crime was up too, by 16%, according to figures published by the force's oversight body, the Scottish Police Authority (SPA).
Police Scotland chief constable Sir Stephen House yesterday attributed some of the rise to more thorough investigations of domestic incidents.
Sir Stephen told a full meeting of the SPA in Glenrothes, Fife, yesterday that almost 400 alleged sexual offences were uncovered in the context of such cases.
He said: "This is one of the reasons we have seen a rise of rape reports of 38% this year. There are other factors too, of course.
"If officers are at a domestic abuse incident and they ask the victim - stereotypically a woman assaulted by a male partner - she will say she has been, say, slapped.
"She is not going to say she has been the subjects of rapes for 10 years."
However, the same victim, he said, may volunteer such information if she is later asked about it.
Officers now routinely follow up domestic abuse cases, a major focus for both police and prosecutors, to see if there has been a sexual crime.
Police also attribute the rise in rape reporting to growing confidence among women and - especially for historic allegations - to the "Jimmy Savile" effect.
Sandy Brindley, National Co-ordinator for Rape Crisis Scotland said: "It is certainly true that victims now have more confidence in the police, thanks to the efforts that have been made to increase reporting, and that will have had an impact on the figures," she said. "But it is also likely there are more of these crimes taking place."
There were 1293 alleged rapes recorded from April to December 2013, compared with 1372 in the 12 months up to April 2013.
Police stressed their detection rate for the crime, when they are satisfied they know who committed it even if prosecutors cannot secure a conviction, has risen.
This accounted for almost three-quarters of the alleged rapes, a rise of nearly 11% on the same period in 2012.
New figures released by the SPA also showed the number of people killed or seriously injured on roads had dropped to 1368 between April and December 2013, a 19% year-on-year drop.
Meanwhile, Sir Stephen denied reports that mobile speed camera vans were being used to "tax" people by issuing speed tickets. "We don't even get to keep the money, which goes to the Treasury," he said. "I don't think it is accurate to say the vans are being used to make money."
l A High Court judge in London yesterday approved a compensation scheme for victims of sexual abuse by Jimmy Savile. The scheme has been agreed between executors of the former Top of the Pops presenter's estate and lawyers for 140 alleged victims.