The charity said the worrying results of its research means that it is time for animal welfare to be taught in schools, so that children understand that mistreating animals is wrong.
Nearly 5,000 acts of animal cruelty and neglect on social media are reported to the RSPCA each year, with more than 500 of those from internet users in Yorkshire, the charity said.
The RSPCA was contacted about animal cruelty on social media by 209 people in West Yorkshire last year, by 196 people in South Yorkshire, by 92 people in North Yorkshire and by 66 people in East Yorkshire.
In the first six months of this year another 123 people in West Yorkshire, 85 people in South Yorkshire, 67 people in North Yorkshire and 29 people in East Yorkshire reported similar social media posts to the charity.
Chris Sherwood, the RSPCA’s chief executive, said: “The number of children seeing animal abuse online is shocking. The current generation of children are witnessing horrifying animal cruelty and neglect through channels which simply didn’t exist for previous generations.
“The risk for children growing up in the 21st century is that frequent and casual exposure to animal abuse will desensitise them and may even make it seem acceptable. Animals need us now more than ever and we want to grow a new generation of young people who care, who are informed and who want to do their best for animals.
“This is why we are launching Generation Kind, an ambitious education programme targeting school children, children in care, young offenders or those at risk of offending and other disadvantaged young people. Central to this is a new campaign to get animal welfare taught in all schools.”
According to an RSPCA poll, 82 per cent of people who responded in Yorkshire said animal welfare should be taught in schools.
Through its Generation Kind programme, the charity will pair disadvantaged young people with mistreated or neglected dogs for a training course about animal welfare and empathy, and to help dogs recover from trauma.
Children faced with difficulties in deprived areas will be offered the chance to engage with animals, animal care apprenticeships will be offered and children aged between seven and 11 will be offered online videos and interactive content to inspire compassion for animals through learning about their needs.
Animal action days will be aimed at children in care, 11 to 14-year-olds will be asked to debate animal welfare and sessions will be run for trainee teachers about teaching children about animals.
Other projects include training members of youth offending teams to help them rehabilitate young people who have harmed animals and recruiting 150 speakers to go into schools, youth groups and clubs to teach children about animal welfare.
The RSPCA said it hopes to reach two million children through its expanded educational programme by 2030.
Mr Sherwood said: “This is the most important campaign we have ever undertaken. We are fighting animal abuse and neglect every day but we can only do so much. If we can foster empathy and responsibility towards animals in the consumers, politicians and decision makers of tomorrow, we can create a society which is truly kinder to animals.”