A very, ahem, magnetic question. Yes, many electric cars do use magnets. An electric motor uses magnets to create motion and this motion is the initial source of energy for the engine. These types of motors are called permanent magnet motors and their magnets are considered rare earth magnets.
However, due to supply issues, there’s been a recent push for motors without magnets such as induction motors. Induction motors use an electric current via copper wiring to create a magnetic field to power the motor. They’re cheaper but less efficient, requiring a larger battery.