We investigate the structure and magneto-transport properties of thin films of the Co₂Cr_0.6Fe_0.4Al full-Heusler compound, which is predicted to be a half-metal by first-principles theoretical calculations. Thin films are deposited by magnetron sputtering at room temperature on various substrates in order to tune the growth from polycrystalline on thermally oxidized Si substrates to highly textured and even epitaxial on MgO(001) substrates, respectively. Our Heusler films are magnetically very soft and ferromagnetic with Curie temperatures up to 630 K. The total magnetic moment is reduced compared to the theoretical bulk value, but still comparable to values reported for films grown at elevated temperature. Polycrystalline Heusler films combined with MgO barriers are incorporated into magnetic tunnel junctions and yield 37% magnetoresistance at room temperature.