By realizing the twistor space of 3d Minkowski space as a hypersurface in higher dimensions we construct a twistor string theory whose single-trace tree-level scattering amplitudes reproduce those of the ABJM theory. The multi-trace tree-level amplitudes describe ABJM theory coupled to conformal supergravity. A byproduct of this construction is the indication that there exist moreN=6 conformal field theories in three dimensions.