The RSPCA said it is a "sad reality" that the charity deals with animal cruelty on a daily basis.
In June, Zouma was sentenced to 180 hours of community service and was banned from owning a cat for five years after pleading guilty to two counts of causing unnecessary suffering to a protected animal.
RSPCA figures show there were 394 calls to its helpline for reporting intentional harm to an animal in South Yorkshire last year – up from 337 in 2020.
There were 551 calls over deliberate cruelty in 2019, meaning there have been a total of 1,282 in the last three years alone.
Intentional harm incidents involve attempted or improper killings, beatings, poisonings, mutilations and injuries or deaths in suspicious circumstances.
Across England, 35,379 calls were made reporting intentional harm over the last three years.
Dermot Murphy, RSPCA chief inspectorate officer, said: "It is a sad reality that we deal with animal cruelty every day here at the RSPCA.
"We are a nation of animal lovers but yet we received over 11,000 complaints of intentional harm through our helpline last year reporting animals from cats, dogs, hedgehogs and everything in between who have sadly been victims of deliberate cruelty.
"We need your help to keep our frontline officers out on the road saving animals and to help us raise awareness that this cruelty is never acceptable."
Mr Murphy also highlighted the rise in intentional harm calls during the summer months – nationally, more calls were taken between July and September than any other three-month period last year.
August was the busiest month for the RSPCA nationally, with 1,041 calls taken – an increase of 10% on the same month the year before.
In 2021, July had the highest number of reports in South Yorkshire, while calls between July and September rose from 83 to 125 year-on-year.