There were a further 90 attempted rapes, down slightly, and 3,008 sexual assaults.
Both police and the Scottish Government believe the rise could be down to increased reporting.
Kenny MacAskill speculated that the publicity generated by the Jimmy Savile case could be responsible for a rise in reports of historic rapes.
“I think undoubtedly we can say it probably is that, but we will have to wait a few years for further research,” he said.
However, Sandy Brindley, of Rape Crisis Scotland, has said it is also possible that more crimes are taking place.
The figure of 1,462 rapes and attempted rapes is the highest since 1976, before which no comparable data is available.
Lily Greenan, manager of Scottish Women’s Aid, said that, while it is hard to say if we are becoming more sexually violent, the culture people are exposed to is. She called for research into links between violent pornography and sexual offences.
She said: “No-one looks at sex offenders coming into the system, young men who are first-time offenders, and what their history is and whether it has involved the use of extreme pornography. That needs to be done.
“I believe there is a link. That is the understanding I have from women who say porn had an impact, that he had been looking at dirty pictures, that is was not unusual for them to be forced to watch porn and then behave like they were the person in the film.”
The Sexual Offences (Scotland) Act came into force in late 2010 and broadened the definition of rape.
It initially led to a reduction in sexual assaults, as some of these crimes were recategorised as rapes, but this group of offences also rose last year.
There has also been a sharp increase in taking, distributing and possession of indecent photographs of children, from 69 in 2009-10 to 225 the following year and 595 in 2012-13.
Police have prioritised sexual crimes since the launch of the single national force, creating a national rape taskforce and 14 specialist divisional teams.
They have also said that tackling abuse in the home will be a key aim.
Deputy Chief Constable Rose Fitzpatrick, head of community policing, said: “It is very important that people feel they can report crime to us, particularly sexual offences.”