Leonardo DiCaprio wears a TAG Heuer Carrera Automatic in the movie Inception. 

The words "swiss made" and "automatic" on the dial and part of the black dial of the watch can be seen in a close-up shot in one of the first scenes in the film. 

The exact model used in the film is the TAG Heuer Carrera Automatic WV211B.BA0787 with steel case, steel bracelet and black dial. The watch has a Calibre 5 automatic movement, date window at 3 o'clock and luminous, diamond-shaped hands.

The best place to find this exact watch is on Chrono24:

Shop at Chrono24 ($1,000 - $2,095)
Pre-owned

Also sometimes available on eBay:

Shop at eBay ($1,277 - $1,830)
Pre-owned and refurbished

It's no surprise Leonardo wears a TAG Heuer: he's one of the brand ambassadors of the brand and can be spotted in several advertisements.

On several premieres of Inception (in London and Tokyo for example), DiCaprio wore a TAG Heuer Carrera Automatic Chronograph Tachymetre with leather strap (CV2016.FC6205).