The terrestrial planets endured a phase of bombardment following their accretion, but the nature of this late accreted material is debated, preventing a full understanding of the origin of inner solar system volatiles. We report the discovery of nucleosynthetic chromium isotope variability (μ54Cr) in Martian meteorites that represent mantle-derived magmas intruded in the Martian crust. The μ54Cr variability, ranging from -33.1 ± 5.4 to +6.8 ± 1.5 parts per million, correlates with magma chemistry such that samples having assimilated crustal material define a positive μ54Cr endmember. This compositional endmember represents the primordial crust modified by impacting outer solar system bodies of carbonaceous composition. Late delivery of this volatile-rich material to Mars provided an exotic water inventory corresponding to a global water layer >300 meters deep, in addition to the primordial water reservoir from mantle outgassing. This carbonaceous material may also have delivered a source of biologically relevant molecules to early Mars.