Victor, the protagonist in Mary Shelley's Frankenstein, most certainly believes in fate. Victor, only known as "the stranger" in Letter IV, states his belief in fate when dialogue between him and Walton is detailed in the letter to Walton's sister, Mrs. Saville.
Victor, after coming aboard Walton's expedition ship, is found to be very ill. After a few days of recovery, Victor begins to tell Walton about his history. Prior to this, Victor asks Walton to hear his tell so that he can offer Walton a warning about being overly ambitious.
Victor's belief in fate is openly stated when he states the following:
“I thank you,” he replied, “for your sympathy, but it is useless; my fate is nearly fulfilled. I wait but for one event, and then I shall repose in peace."
The fact that Victor knows his end is near speaks to his belief in his fate, which is his death.
While it is not clear whether or not Victor believed in fate over the course of his trials and tribulations, one can assume that either his troubled life brought upon his belief in fate or his trust in signs (exampled by his interest in science stemming from the lightning strike to the tree). Regardless of when he began to believe in fate, his statement in Letter IV proves his belief.