The row follows the inaugural world championship for eating guga, as the birds are known in the Hebrides, which was held on Lewis in December last year and has caused outrage among some environmentalists.
The practice, which was once common in other parts of northern Britain and Ireland, notably St Kilda, has been defended by Scottish Natural Heritage which claims it is legal and the bird numbers are actually increasing at the hunt site.
The petition was the idea of Care2, a North American social network website which styles itself as the "Largest online community empowering people to lead a healthy and green lifestyle".
It was founded in 1998 by campaigner Randay Paynter who says his life's mission is "To be a Force for Good". His causes include endangered species, same sex marriage and rain forests.
The petition says Scotland has tougher conservation and animal welfare laws than the rest of the UK. It states: "This makes it all the more shocking that a grotesque gannet chick eating contest has started on the Isle of Lewis in the Outer Hebrides, organised by a local football club. Contestants race to guzzle half a chick in the least amount of time. This would be illegal anywhere else in Scotland - seabirds are protected. But the residents of Ness district get a special licence to slaughter some 2000 gannets a year, supposedly in the name of tradition. Hitting gannet chicks with sticks is a 'tradition' we could do without."
It calls on the Western Isles Council to ban the killing of the birds.
Ten men from the Ness area of the island are allowed to kill 2000 guga during their annual August trip to Sula Sgeir, the narrow rock with 300ft cliffs which lies 40 miles to the north.
The birds are taken using the same basic method handed down through our centuries. Working in pairs, the men grab the birds from their nests with a long pole, catching them around the neck with a rope noose. They then pass them back to a colleague who knocks them on the head with a stick.
A council spokesman said it had no role in licensing the guga hunt which is done by Scottish Natural Heritage.
In 2010 Scotland's leading animal charity, the Scottish SPCA attacked the guga hunt as "barbaric and inhumane". But the men of Ness have long argued that that said grouse shooting causes the birds greater suffering, but does not attract the same condemnation.
An SNH spokesman said it recognised the guga hunt's cultural and historical significance and it was unlikely that taking 2000 birds would have an adverse effect on the local gannet population. He said the licence included a condition to ensure the birds were humanely dispatched, and continued: "We undertook a count of the Sula Sgeir population last summer which showed a final count of 11,230 sites apparently in occupation. This represents a 2.2% per annum increase on the last count of 9225 in 2004. The UK and Scottish gannet population is also increasing and this leads us to conclude that the hunt in its current form is sustainable."