Is it possible to play Star Wars Battlefront 2015 on Oculus Rift?

You cannot play Star Wars Battlefront on a VR platform

To play a game on any VR platform, such as the Oculus Rift, the developers have to program their game specifically for that platform. This means that unless EA release a VR version of the game, which isn't likely to happen, you won't be able to.

This doesn't mean that all non-VR games cannot be played on a VR headset, there are quite a few games that have been converted to VR. For instance, Minecraft have released a VR edition of the game.

You can play games using a VR headset on some platforms

On the PS4 there is a cinema mode which allows you to play any non-VR game in VR using the PlayStation VR headset. According to PS VR website:

All non-PlayStation VR PS4 games are playable in cinema mode with the PlayStation VR headset. Cinema mode lets you experience your non-VR games on a simulated big screen while wearing your VR headset.

There is a similar thing that you can do on a PC using Steam, however this requires a third party program that you can buy through Steam. One of these apps, Big Screen, simply creates a virtual desktop in a VR world and runs your games. Another, Virtual Desktop, does a very similar thing to Big Screen in that it creates a desktop in a VR room. However, it also has the functionality to create a much more immersive environment with a dynamic 3D background and the desktop all around you. Unfortunately, these do not allow you to go into the game with it all around you, they only display an image of the game in a VR world.

Unfortunately, I couldn't find anything like these for the Xbox. Thus, leading me to believe there is no option for you to play Star Wars Battlefront in VR.