Michelle Boyd started the petition after concern for her own welfare grew while out walking a new puppy she got just seven months ago.
She found reports of violence and attempts at dognapping were on the increase as the cost of a puppy can be up to £3,500 – also leading to a rise in puppy farms with apparent links to organised crime.
Ms Boyd, from Balloch in West Dunbartonshire, said she only expected “my best case scenario would have been if I managed to get 5,000 signatures”.
She added: “I looked into it and I saw that the penalties for dog thefts are completely inadequate – if someone steals your dog it’s treated the same as if they steal your mobile phone and the most common penalty’s usually a £250 fine.
“I just started the petition to see how much traction it would get; the point behind it is a view to trying to get sentencing for people that steal dogs to be much more appropriate and for the crime of dog theft to be a specific crime.
“Particularly in the pandemic dogs are companions to people that live on their own, they’re part of the family, one of the few things you could do during the pandemic is walk your dog and you didn’t even feel comfortable doing that because you were scared, somebody was going to leap out of a van and steal them.
“I’ve had support from a local politician who is prepared to offer more once the election is over but I would really like to see it go to parliament and be properly debated, and the for the justice department to look at what sentences are being handed out.
“The bill was passed about increasing sentences for animal cruelty to go from a minimum of six months to now it’s five years so there is a wee bit of momentum about this.”
Ms Boyd admitted she walk her dog far on her own and instead wait to go out with her husband.
She added that some friends will not let their children walk their dogs because of fears which has “spoiled the experience”.
Through the petition she has had others sharing stories including people posing as BT engineers and marking people’s houses as part of dognapping schemes.
However Ms Boyd also said she has heard of people taking matters into their own hands to avoid being the victim of a dog theft.
She said: “A lot of people when I’m out walking my dog say how scared they are, but also people are slightly taking things in their own hands and then arming themselves.
“One lady I bumped into in the park was walking her dog carrying a cooking blowtorch and I said to her ‘if you use that on somebody the penalty for that will be far worse than the person that tries to steal your dog’.”
The petition can be found online at https://www.change.org/p/scottish-government-stronger-penalties-for-dog-theft.