The number of reported rapes increased by 35% to 905 between April and September, compared to the same period last year. The number of robberies fell 25% to 727 in that time.
Police Scotland is now working with nightclubs and bars to train bouncers to tackle "late night predators" who single out vulnerable young women by buying them drinks to isolate them from their friends on nights out.
Despite significant decreases in violent crime across Scotland, there has been a sharp rise in sexual offences.
Chief Constable Sir Stephen House, who believes only about half of all rapes are reported to the police, said: "We are seeing something very strange happening. Rape used to be a very infrequent offence to see. Now we are seeing it much more often."
Speaking exclusively to The Herald, he said: "Every Monday we sit down as a management team and it is not unusual to find that there are more rapes than robberies across the country.
"We have had 905 rapes so far this year [since April]. We have had 727 robberies. Robbery is 25% down on the same time last year. Our detection rate for robbery is remarkably good and criminals know that. It has been coming down for a number of years."
Police believe some of the increase in reported rapes can be attributed to greater confidence among victims and the publicity around the Jimmy Savile abuse cases.
Sir Stephen said: "Because of the Savile case, victims have realised the police will take it seriously, and there is no statute of limitation and they can still report it even if it happened 10 years ago," said Sir Stephen.
"Partly as a result of taking domestic abuse more seriously we are getting more rapes reported. When you start taking a statement at a domestic abuse incident the first thing said is not that the person has been raped. What is going to happen is that they're going to talk about being shouted at and beaten up. Then what's going to happen is that they're going to say they've been raped repeatedly for the past five or ten years. That is how it would come out. We're seeing more for that reason.
"We want more people to come forward. We have got far more people involved in tackling rape and sexual offences now. We've got experienced and professional detectives working on this. A senior officer will review all undetected rapes and ensure we are not writing things off.
"The training and attitude has changed dramatically across the country. We will investigate all allegations properly. We've very keen for victims to come forward even if the chances of a conviction are low. We will always investigate and try to secure a conviction. Our figures suggest we are seeing probably less than half [of cases reported]."
Police are working with nightclubs and bars to ensure bouncers are trained. Beat police are also being encouraged to intervene if they see a vulnerable woman with a stranger.
"The scenario we are trying to do more about is the late night predator," said Sir Stephen.
"You're in a nightclub or a pub, a group of girls who have all had too much to drink probably, and all of a sudden a man appears and is buying a drink for one girl. Often people are not thinking clearly and they think one of them knows this guy.
"But he is a total stranger who has decided to buy someone a drink to isolate them. He puts his arm around her and starts talking to them and before you know it he's ushering her away to a taxi.
"The friends are left thinking she has gone off with that guy that she must know. If you were out in the middle of the day would you get into a taxi with a man you had just met? Of course you wouldn't. That is the vulnerabilty.
"Under the Best Bar None Scheme we are getting licensees and door staff the training and confidence to intervene and challenge this. If they question the situation, that is usually enough to get the guy away on his toes."
Sir Stephen said he wanted to see far more of these kind of initiatives drawing on the experience of door staff.
He added: "A member of the public doing it might end up in a fight. Our cops do it too. We encourage them too if there is the slightest suspicion they don't know each other then they're straight in there."
Scotland has been criticised for its low conviction rate for rape cases. Previously, the Crown Office has revealed 33% of rapes indicted to court lead to a conviction. However, only 10% of incidents reported to the police actually go to court. Of the total number reported, approximately 3% lead to convictions. The Crown Office says the figure does not compare like with like.