Social media "crimes" have increased by one-third since 2011, with complaints to police forces in England and Wales increasing from 9,917 to 13,019 in 2013.
It follows a number of high-profile incidents in which either threats were made or comments some people considered "offensive" were reported.
Reports of crimes involving Twitter doubled, from 677 to 1,291, while Facebook "crimes" rose from 9,917 to 13,019.
Hampshire and Kent, for some reason, appear to have the most complaints. Hampshire had 3,681 reports regarding Facebook in 2013, and 187 over Twitter. Kent, meanwhile, filed 3,528 complaints over Facebook and 626 over Twitter.
These two counties even beat the Metropolitan Police, Britain's biggest police force covering the capital. It filed 1,219 complaints over Facebook and 154 over Twitter.
The figures were unearthed in Freedom of Information reports filed by think tank Parliament Street, and covering 25 police forces. It said that the figures indicated that the government ought to do more to tackle crimes related to social networking sites.
It wants every police officer to be trained in cyber skills and tougher sentences for online offences "to ensure criminals do not gain the upper hand".
However, privacy campaigners suggested that crimes committed online should be treated no differently than if they had been committed in public.
"The last thing we need is the police spending more time snooping on people's tweets and abandoning all common sense because something involves new technology. Social media is an essential part of how people communicate and crimes should be prosecuted the same whether it happens on or offline," Big Brother Watch's Nick Pickles told the Daily Mail.