The clip is said to have been filmed in Mowbray Park in Sunderland and appears to show a group of three teenage girls in the bushes, with one launching blows in the direction of a swan and goading the bird.
Northumbria Police has confirmed it has launched a probe into the incident.
Inspector Jamie Southwell said: “We are aware of footage circulating on social media which appears to show a swan being attacked in Mowbray Park.
“This kind of behaviour is totally unacceptable and a full investigation has been launched.
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“We would encourage anyone with information regarding the incident to contact police at 101 quoting reference 1122 230618 or Crimestoppers anonymously on 0800 555 111.”
A spokeswoman for the RSPCA added: "We are so grateful to people who report suspected animal suffering to us and we would like to reassure people we will always look into and, if necessary, investigate any complaints made to us about animal welfare.
“Unfortunately we are unable to discuss complaints about specific people and what action may have been taken.
"We understand how frustrating that is for animals lovers but releasing information could prejudice a future prosecution or could lead to us being fined.
“A lot of the time issues will be dealt with by advice and education and it is not always appropriate to publicise this information for legal reasons.”