People's Daily also shared a screenshot of the video, which shows the cat having patterns and the Chinese character "endurance" tattooed to its right foreleg.
"Qiangzi" apparently told a reporter that "tattoo is a form of art" and he wanted to give it to his pet.
The man gave the cat anaesthetics after shaving the fur off its leg.
"Qiangzi" explained to MailOnline that he inserted semi-permanent ink into the kitten using an eyebrow tattoo pen.
"The ink contains plant extract and will cause no harm to the animal. The tattoo will fade out as skin changes over time," he said.
He said the anaesthetics dosage had been used according to the veterinarian standard.
He said that he had used the anaesthetics very carefully: "I bought the anaesthetics from an animal hospital and an excessive dosage of it could kill my cat."
"Qiangzi" first posted the video to a closed messaging group on social media. He has deleted the footage since.
However, a screenshot of the video has been widely shared by the public last week as people criticised the man for his "cruel" behaviour.
One web user with the screen name 'secretamente' said on Weibo: "Did you have the cat's permission before doing this?"
Others said there were many other ways to practise tattooing and that it was not necessary to do it on a cat.
"Nikandouwodishi" wrote on the artist's Weibo account: "You can practise on a piece of pork, or even buy synthetic skin on Taobao. Why did you do it on an animal?"
Apparently, the tattoo artist has realised his fault.
He claimed on his Weibo account that he had taken the cat to Zhangying Stray Animal Rescue, a nearby animal rescue centre, to beg forgiveness from the public.
He also said that he still wanted the cat back, so he had donated 50 yuan ($10) to the animal rescue centre and asked for permission to take the animal home.
Zhu Enxia, 55, the founder of the rescue centre, confirmed to MailOnline that the cat was being looked after by them.
A video sent by Ms Zhu shows the cat recovering as the tattoo faded.
"I sterilised its wounds every day and the fur on its leg are growing out already," Ms Zhu said.
She also stated that she would not give the cat back to the tattoo artist. The cat is waiting for a new owner.
Jason Baker, the Vice President of PETA Asia said abusing animals is not art.
Mr Baker said: "Even though the cat this person has abused were supposedly anesthetised while receiving the tattoos, these procedures were still unnecessary and painful, and could lead to complications that endanger the animals' health."
Dr Manilal Valliyate, a veterinarian and chief executive officer at PETA India, commented that the skin is a very sensitive organ.
He said: "Not only would tattooing damage these delicate structures, any resulting injury or infection would also compromise the skin's role as the body's first-defence system.
"It's highly unethical and cruel to subject animals to procedures that offer them no benefit and only cause them harm."