The group has written to the East Lothian Council to ask for planning permission for the tribute.
Their planned design will read: “In memory of the pigs who suffered and died in a lorry accident at this spot. … Try vegan."
Elisa Allen, PETA Director said: "For nothing more than some chops, this crash left animals suffering on an already terrifying trip, likely to the abattoir
"PETA's roadside memorial can prevent further tragedies, including human ones, by reminding people to drive with care and spare a thought for animals by no longer eating them."
The group opposes speciesism and their motto reads, in part, “animals are not ours to eat.”
The A1 crash happened on Monday, November 16 and involved three vehicles.
Local gamekeeper Thor Søndergaard said that shortly after the crash he was contacted by a police officer that he knew who asked him to come and assist.
He said that the noise of the trapped pigs was deafening, and that he could see dozens of the pigs “suffocating” inside the truck and “lying on top of each other”, but officers at the scene told them not to remove any other animals.
A Scottish Fire and Rescue Service spokesperson said: "We were alerted at 10.33am on Monday, November 16 to reports of a road traffic collision on the A1 near the village of Cockburnspath in the Scottish Borders.
"Operations Control mobilised five appliances to the scene of the incident involving four vehicles, one of which was well alight and contained a number of livestock.
"This was a challenging incident, therefore it was important to release the animals in a controlled way due to the location, which was in close proximity to the East Coast Main Line.
“Crews received professional advice from our partners at the Royal (Dick) School of Veterinary Studies via telephone prior to their attendance at the scene.
“When on scene, firefighters worked jointly with the vets to care for the livestock as they were safely released and transferred to an awaiting vehicle, but unfortunately, despite combined efforts, a number of them were lost.”