ipole is a ray-tracing code for covariant, polarized radiative transport particularly useful for modeling Event Horizon Telescope sources, though may also be used for other relativistic transport problems. The code extends the ibothros scheme for covariant, unpolarized transport using two representations of the polarized radiation field: in the coordinate frame, it parallel transports the coherency tensor, and in the frame of the plasma, it evolves the Stokes parameters under emission, absorption, and Faraday conversion. The transport step is as spacetime- and coordinate- independent as possible; the emission, absorption, and Faraday conversion step is implemented using an analytic solution to the polarized transport equation with constant coefficients. As a result, ipole is stable, efficient, and produces a physically reasonable solution even for a step with high optical depth and Faraday depth.