We report the first experimental demonstration of a plasma wave plate based on laser-induced birefringence. An elliptically polarized input was converted into a nearly ideal circularly polarized beam using an optical system composed of a second laser beam and a plasma. The results are in excellent agreement with linear theory and three-dimensional simulations up to phase delays exceeding π/4, thus establishing the feasibility of laser-plasma photonic devices that are ultrafast, damage-resistant, and easily tunable.