In a video published by The Sun, Zouma could be seen picking up the family pet before kicking it across the kitchen floor. The video was originally published on Snapchat by Zouma's brother, Yoan.
The defender later apologised for his actions, which resulted in him being fined two weeks' wages and his two cats being taken into care.
The RSPCA said in a statement on Wednesday: "Following a full and thorough investigation, we have started the process of bringing prosecution proceedings against Kurt Zouma and Yoan Zouma under the Animal Welfare Act. The two cats continue to be cared for by the RSPCA. We will be in a position to release more information once a court date is confirmed."
West Ham said they were aware of the RSPCA statement and said Zouma was cooperating fully with the investigation.
"It is our understanding that Kurt's cats have been checked by a vet, are in good health and have suffered no physical injuries," the club said in a statement.
"For legal reasons, neither Kurt or the club will be making any further comment at this time."
Despite calls for the defender to be dropped following the video's release, West Ham boss David Moyes continued to select Zouma.
The move caused one of the club's sponsor's Experience Kissimmee to end its partnership with the club, while another sponsor Vitality, the club's official wellness partner, suspended their deal.
Zouma was also dropped by his boot sponsor Adidas.
Yoan had been dropped by his club Dagenham & Redbridge after the allegation last month but the fifth-tier side said he will now be available to play.
"Dagenham & Redbridge FC note the decision of the RSPCA to charge Yoan Zouma under the Animal Welfare Act 2006," they said in a statement.
"Four weeks have now elapsed however since the incident, and the club feels that any further suspension from the team would be detrimental to both the Club and Yoan. A decision has been made therefore for Yoan to be available to play."
Information from Reuters contributed to this report.