Amos Price, 30, was seen dragging his dog towards the white and black cat sitting on a garden wall in Walsall in CCTV footage.
Before letting go of the lurcher's collar, he looked around to check he was not being watched and pulled his hood up over his baseball cap.
On being freed, the dog leapt up and pulled the terrified cat, called Cleo, off the wall with his teeth and savaged her to death.
The father-of-two was arrested after video footage of the attack in Woodlands Crescent, Pelsall, on October 23 was released by police.
When his cat failed to return home the following day, Gary Truefitt checked his security camera and was horrified to discover the fate of his long-time companion, said Ms Helen Shipley, prosecuting at Walsall Magistrates Court.
Price, of Trevor Road, Pelsall, pleaded guilty to causing unnecessary cruelty to a protected animal.
Passing sentence, Mr Brian Benton, chairman of the magistrates, who imposed the maximum sentence given Price's guilty plea – 18 weeks, said he would have jailed him for longer if he had not been restricted by the law.
Price was also ordered to pay £250 compensation to Mr Truefitt and a £122 victim surcharge to the court, and was disqualified for life from keeping an animal.
Mr Truefitt told BBC WM: "It's not long enough, it needs to be over 12 month I think at least.
"I know the RSPCA are trying to get a longer sentence for him.
"To go around and do that deliberately to somebody's pet it's disgusting, and to me he's got away with it."