No, Bram Stroker had nothing to do with the infamous bet that produced Frankenstein.
The idea of Frankenstein came up when the married Romantic poet, Percy Bysshe Shelley took his then girlfriend Mary (:) can't remember maiden name) to Geneva so they could vacation with other famous Romantic, Lord Byron. The three were one day trapped inside their cabin due to a tempestuous storm. The three, stuck inside, went about telling each other stories. Mary, later to be Mary Shelley, "won" the competition by making up the story of Frankenstein.
Mary Wollstonecraft Godwin (later Mary Shelley) couldn't come up with anything at the time. She later wrote her novel, inspired by the contest. She started it as a teen and finished it in her early twenties.
Stoker (not Stroker) was not involved with the contest. Trivia: Dracula can be read as a book about syphilis, then raging through Europe in a far more virulent form than the current. Syphilis probably killed Stoker, though that's unproven.
Just a fun fact, the legendary night as mentioned by silt is depicted in the bizzarre, 1980 B- Movie, "Gothic". To add to the lore of that infamous gathering, John Polidori, Lord Byron's physician, was supposedly present and conceived his story, "The Vampyr" on that same night. Of course, I cannot aptly speak for the integrity of the film, but if you take an interest in literature, you may find the film amusing. Just don't take it too seriously. :)
Your statement made me laugh out loud. Especially owing to the fact that the person posing the original question could've done a google search in about a minute to realize their question wasnt valid. Thank you.