He was seriously injured in a bomb attack in Afghanistan in 2006.
Since carrying the torch on 26 June, Doncaster-based L/Bdr Parkinson has had thousands of requests on Facebook.
But the site limits friend associations to 5,000 per personal page and he cannot accept all the requests.
Flanked by hundreds of people, he walked for nearly half an hour with the Olympic torch with an assistant who supported his arm.
L/Bdr Parkinson's nomination stated: "The brain injury took his speech, but not his personality and sense of humour," adding he now speaks unaided.
It said: "Determined to prove everyone wrong, he fought back every step of the way. Ben's intelligence and wit [are] unchanged. Still the same funny and caring Ben."
He spends 12 hours a day in the gym and rehab and walks with crutches, spending "the rest of his time spent raising money for many military charities and as patron of his beloved  
          Pilgrim Bandits
".
L/Bdr Parkinson's mother Diane said the responses had "been phenomenal" and that Ben was really "buoyed up" by the support and friendship he had been shown.
She said: "It's just unbelievable, Ben's had way over 5,000 friend requests but Facebook won't let him have more than that number.
"Thousands of people have joined the Pilgrim Bandits website and the messages of support we've had are great.
"Ben's page has had 19,000 hits just on an update, I don't understand how these things work, but it's phenomenal."
She said the amount of post the family had received had also increased.
She added: "Some mail has just been addressed to Ben, please Mr Postie.
"E-mail traffic has gone through the roof and Ben's had hundreds of requests to visit places with the [Olympic] torch.
"He's absolutely bouncing and buoyed up and elated."
Facebook would not comment on the issue but their guidance was that if people were receiving this many requests then they have become a public figure, so should consider having a page instead of a profile.
Alternatively, Ben could use subscribe so that people can see his public updates without actually becoming a friend.
A total of 8,000 people will carry the flame during its 8,000 mile, 70-day journey to the opening ceremony of the Olympic Games in London on 27 July.
Injured paratrooper Ben Parkinson, who carried the Olympic flame, has been swamped with friend requests on social media and seen a huge increase in post addressed to "hero Ben".