Nope. He never won any Oscars though he was nominated for the following:
2008: Best Performance by an Actor in a Leading Role
for: Sweeney Todd: The Demon Barber of Fleet Street
2005: Best Performance by an Actor in a Leading Role
for: Finding Neverland
2004: Best Actor in a Leading Role for: Pirates of the Caribbean: The Curse of the Black Pearl
According to IMDB.com, he has won the following:
2000: Blockbuster Entertainment Award, Favorite Actor - Horror for: Sleepy Hollow
1999: César Awards, France, Honorary César
2006: Empire Awards, UK, Best Actor for: Charlie and the Chocolate Factory
2004: Empire Awards, UK, Best Actor for: Pirates of the Caribbean: The Curse of the Black Pearl
2008: Golden Globes, USA, Best Performance by an Actor in a Motion Picture - Musical or Comedy for: Sweeney Todd: The Demon Barber of Fleet Street
2003: Hollywood Film Festival, Actor of the Year
2004: Irish Film and Television Awards, Audience Award, Best International Actor for: Pirates of the Caribbean: The Curse of the Black Pearl
1996: London Critics Circle Film Awards, ALFS Award, Actor of the Year for: Ed Wood, also for Don Juan DeMarco.
2007: MTV Movie Awards, Best Performance for: Pirates of the Caribbean: Dead Man's Chest
2004: MTV Movie Awards, Best Male Performance
for: Pirates of the Caribbean: The Curse of the Black Pearl
He has also won People's Choice Awards, Rembrandt Award, Russian Guild of Film Critics Golden Aries, Screen Actors Guild Award, and Teen Choice Awards.