Can a US citizen adopt a dog in Canada?

The dog must first be registered to the original owner (usually the breeder) with the American Kennel Club. A US-born puppy cannot be registered with the Canadian Kennel Club until it is registered with the AKC. If the pup is sold before being registered, the original owner signs the Transfer of Ownership on the registration application and the new owner gets the registration papers in their name.

The dog must first be registered to the original owner (usually the breeder) with the American Kennel Club, then

The dog must be registered with the American Kennel Club like any other AKC-eligible American-born pup. The breeder either registers the pups or signs the appropriate application for registration, with details of the breeding date, birth date, sire and dam's names and registration numbers. If the breeder (original owner) also signs the transfer of ownership on the registration application, the new owner will get the registration papers in their name.

That is how a US born puppy gets registered with AKC, no matter where it lives.

If the owner then wishes to register the dog with the Canadian Kennel Club, they will need the AKC registration papers in their name, an official 3-generation pedigree from the AKC, and an Application For Registration Of A Foreign-Born Dog from the CKC.