Here are three racing games for Linux, on this article I assume you use Ubuntu:

VDRIFT

Want realistic racing? Then you need to try VDrift. First released in 2005 by Joe Venzon and inspired by Gran Turismo, Venzon created a simple racing game powered by the Vamos Automotive Simulator. Two years, three programmers, and a ton of code later, it’s got extremely realistic physics, 28 cars, 19 tracks, AI players, networking, and great looking graphics.

VDrift hasn’t (yet) made it into the Ubuntu repositories (though the data package made it in. Odd). Luckily, GetDeb includes an Ubuntu package for it.

TORCS

If you want a powerful racing game, look no further than TORCS, The Open Racing Car Simulator. It’s gone from a 1997 2D soapbox derby simulator to a powerful 3D racing game with championships, tons of tracks, a thriving community, and all the third party tracks and cars you can download. There are even two online championships: TORCS Driving Championship and
The TORCS Racing Board.

To install TORCS, just use your favorite package manager (apt, aptitude, Synaptic, Adept, etc) to install the ‘torcs’ package from the universe repository.

TRIGGER

If arcade-style racing is your style, give Trigger a try. It’s simple: they give you a car, and you have to navigate a tricky path full of off-road terrain with an extremely tippy car.
Go too fast, and you risk flipping off of the road. But move too slowly, and you risk being dominated by your cunning AI opponents.

To install, just use your favorite package manager to grab the ‘trigger’ package in
the universe repository.