Police Scotland said more than 160 people reported being raped in the very early stages of dating in 2018/19.
This meant almost 11 per cent of rapes committed by someone other than a partner or ex-partner happened on a first or second date after the two people met online or in a social setting beforehand.
Officers said the 160 figure was a "shocking statistic", particularly when the number of incidents is likely to be "significantly under-reported".
Assistant Chief Constable Gillian MacDonald, from the Major Crime and Public Protection Unit, said: "No-one should go on a date expecting or feeling entitled to sex, just as no-one goes on a date expecting to be raped.
"Nor should anyone feel bullied, coerced or shamed into having sex because their date expects it or believes they're entitled to it because they paid for drinks or dinner.
"Our new campaign seeks to tackle these issues head on and make it clear that sex without consent is rape."
While the rise in dating apps and websites has led to an increase in the number of people meeting online, police warned no-one meeting this way should feel entitled to sex.
The campaign is aimed primarily at men aged 18 to 35, which police said is the peak age for offending.
The £30,000 initiative will run for six weeks from 2 September on various social media platforms, on telephone kiosks and in toilets in clubs.
"Sex without consent is rape and that consent must always be free and willing, not something assumed or given through pressure or coercion.
"This campaign is a welcome contribution to the national conversation we need to be having about sex and consent.
"What needs to be clear - and it cannot be said enough - is that it doesn't matter what the situation is, all sexual violence, abuse and harassment is unacceptable."