The dog breeding website Designer Mixes says that the combination of pit bulls and dachshunds is called a Doxbull or a Pitwee and can weigh about 11kg when fully grown.
The Humane Society says that Rami is "full of energy" and doesn't "listen very well, so you'll need to take some time to train me. Because I tend to be a bit hyper".
Rami's ears have also been cut for an unknown reason.
Potential owners will need to go through an interview process and pay for the canine's vaccinations before taking him home.
Photos and videos of the dog have been shared more than 40,000 times and generated more than 9,000 comments since last week, most of which say that Rami is adorable.
Some commenters were unconvinced and thought that the pictures were doctored or that the animal was not a mix but actually has canine dwarfism, a condition that affects dogs' growth and spines.
Others were not impressed by the dog's unique appearance, saying Rami is "freaky looking".
Fears remain that the overwhelming interest in Rami will lead breeders to try and manufacture more unnatural designer mixes, which often have health problems.
For those that may be disappointed by missing out on adopting Rami, the Moultrie Colquitt County Humane Society says there are many more unique animals at shelters across the country.
- Daily Mail