Spin density waves (SDWs) are antiferromagnetic ground states characterized by real-space spin modulation. When an electronic system undergoes a paramagnetic-SDW transition, the translational symmetry is spontaneously broken and energy gaps are developed near the Fermi level, which offers potential for constructing various SDW components. Here we report a prototype resistive memory device based on a prototypical SDW metal, antiferromagnetic chromium. Transport and magnetic measurements show that the paramagnetic-SDW transition, i.e., the SDW antiferromagnetism, can be effectively suppressed by the electric-field-generated piezoelectric strain in epitaxial Cr/0.7Pb(Mg1/3Nb2/3)O-3-0.3PbTiO(3) (PMN-PT) heterostructures. This enables a large electroresistance effect for metallic systems as the SDW band gaps can be intentionally controlled to vanish or develop. Combining this electroresistance effect with the different remanent piezoelectric strain of PMN-PT after poling by electric-field pulses of opposite polarity, we obtain two nonvolatile resistance states differing by about 1.8% and stable against a magnetic field of 3 T at room temperature. Our work unveils the electric-field controllability of the SDW transitions in thin films and the consequent wide application prospects of SDW materials.