The petition, created four days ago on Change.org website, has gathered more than 89,000 signatures so far.
"We demand a revote be taken of said referendum, where each vote shall be counted by two individuals, one of whom should be an international impartial party without a stake in the vote," reads the petition, addressed directly to the outgoing First Minister of Scotland Alex Salmond.
The document has to be signed by no less than 150,000 people to be sent to Salmond.
Another petition, published on 38degrees.org.uk and addressed to the British Parliament, received more than 63,000 signatures in three days. It needs to be signed by 12,000 more people to be submitted for Parliamentary consideration.
"Investigate the vote counting procedures. Allow an independent re-count of all vote," the petition demands.
The Scottish independence referendum, in which 55.3 percent of Scottish voters backed continued membership of the UK, took place on September 18. On September 19, the leader of the pro-Scottish independence Scottish National Party (SNP), Alex Salmond, announced his decision to resign as leader of his party and First Minister of Scotland.