You can play Rainbow Six Siege for free using the Steam or Uplay platforms. The game is free starting today and will be so until April 18th. Moreover, after the end of the period, you can buy the game with a 30% off for the standard edition and 40% off for the Gold Edition.
Here is the Steam link. To add a free version of the game to your library, scroll down the page until you will see the "FREE WEEKEND" line. It is situated between the 3 posters promoting the game's free week. You would like to click on the poster that is under the "FREE WEEKEND" line.
If you are the Uplay user, open the client and search for the banner advertising the free weekend event.
Here is an explanation video for you, in case you are having troubles finding the right Steam link: