High quality thin films of La_0.67Ca_0.33MnO₃ (LCMO) of different thickness were grown on LAO substrates by pulsed laser deposition (KrF, λ = 278 nm). The AFM images suggest a twodimensional step-growth. DC magnetization measurements of the films in a field of 500 Oe show that the magnetic ordering temperature is the same for all the films in both FC and ZFC conditions and is the same as that for the bulk. However, a difference is seen between the FC and ZFC magnetization of the films. There seems to be a systematic in this difference with respect to the thickness of the film, with the difference decreasing with thickness. We suggest that the difference in the magnetization under FC and ZFC conditions may be due to strain-induced anisotropy arising from the lattice mismatch between the substrate and the film or due to the shape anisotropy due to epitaxial growth