A post on the PlayStation blog has confirmed that the DeLorean will be available on October 21st (just in time to see Marty McFly driving into the current day) for $1.99.
The Vice President of marketing for Psyonix, Jeremy Dunham, had this to say:
This will not be the only set of DLC coming out for Rocket League this month, as the Revenge of the Battle-Cras pack will also be out this October - bringing two new cars and over a dozen new accessories to the game.
Nor is this the only Back to the Future content coming out in gaming this month. Telltale’s Back to the Future game is getting a rerelease on the PS4, Xbox One, and Xbox 360 to celebrate the 30th anniversary of the Back to the Future series.