X-ray powder diffraction with a femtosecond time resolution is introduced to map ultrafast structural dynamics of polycrystalline condensed matter. Our pump-probe approach is based on photoexcitation of a powder sample with a femtosecond optical pulse and probing changes of its structure by diffracting a hard X-ray pulse generated in a laser-driven plasma source. We discuss the key aspects of this scheme including an analysis of detection sensitivity and angular resolution. Applying this technique to the prototype molecular material ammonium sulfate, up to 20 powder diffraction rings are recorded simultaneously with a time resolution of 100 fs. We describe how to derive transient charge density maps of the material from the extensive set of diffraction data in a quantitative way.