Sonic Drift is the first racing game in the Sonic the Hedgehog franchise. Players control one of four characters―Sonic the Hedgehog, Miles "Tails" Prower, Amy Rose, and Doctor Eggman―and race around a series of tracks, with the objective being to cross the finish line in first place. 18 tracks are featured, based on the various zones of 1991's Sonic the Hedgehog, including the Green Hill Zone. Drift is the first Sonic game to feature Amy as a playable character.

There are three game modes: Chaos GP, a grand prix mode; Free Run, a practice mode; and Versus Mode, where players can compete with one another. Chaos GP contains three separate cups of six tracks each and a points system where the goal is to earn more points than the competition. Each cup is identified with a color: green, yellow, or red.

The gameplay of Sonic Drift shares similarities with Sega's "Super Scaler"-type arcade games such as Out Run and Super Monaco GP, although with inspiration from Nintendo's Super Mario Kart. Each character has strengths and weaknesses; for instance, Sonic has fast acceleration but poor control, while Eggman has poor acceleration but moves at high speed. The top half of the player's screen shows the course map, while the bottom displays the player's car racing around the track. The game's driving mechanics focus on drifting to steer around corners at speed. Driving into television monitors scattered around the track awards the player a power-up, such as invincibility. Tracks also contain gold rings that can be collected to use a special move, which is unique for each character; for example, Sonic gets a speed boost, while Tails gets a jump.