The two actors, who are filming the next installment in the superhero franchise together, have both made the shortlist for the coveted trophy - the only BAFTA voted for by the public - which recognises young talent.
Garfield and Stone are nominated alongside British actors Tom Hardy, Aaron Johnson and Gemma Arterton - and the St. Trinian's actress is delighted with the honour.
Arterton says, "I am absolutely thrilled and honoured to be one of the shortlisted actors... 2010 was an incredible year for me and to be recognised in this way by both my peers and the film-going public is amazing. I'm in very good company with the other actors who have been nominated, so it is a huge compliment to be considered to win this prestigious award."
The prize will be handed out at the BAFTAs ceremony in London on 13 February (10).
Previous recipients of the Orange Rising Star honour include The Last King of Scotland actor James McAvoy, Bond girl Eva Green, and Transformers star Shia LaBeouf. Last year's (10) winner was Twilight actress Kristen Stewart.