We report the structural and physical properties of epitaxial Bi2FeCrO6 thin films on epitaxial SrRuO3 grown on (100)-oriented SrTiO3 substrates by pulsed laser ablation. The 300 nm thick films exhibit both ferroelectricity and magnetism at room temperature with a maximum dielectric polarization of 2.8 microC/cm2 at Emax = 82 kV/cm and a saturated magnetization of 20 emu/cc (corresponding to ~ 0.26 Bohr magneton per rhombohedral unit cell), with coercive fields below 100 Oe. Our results confirm the predictions made using ab-initio calculations about the existence of multiferroic properties in Bi2FeCrO6.