We investigate the step decoration growth and magnetic properties of Fe grown on a Pt͑997͒ vicinal single crystal by means of reflection high energy electron diffraction ͑RHEED͒, scanning tunneling microscopy ͑STM͒, and the surface magneto-optical Kerr effect ͑SMOKE͒. Pt͑997͒ has 2 nm wide, ͑111͒-oriented terraces separated by ordered, monoatomic steps along the ͓110͔ direction. The Fe is grown at room temperature as wedges with thickness ranging from 0 to 4 monolayers ͑ML͒. RHEED and STM show that Fe stripes form at low coverage due to step decoration. SMOKE data taken along a wedge indicate that the Fe is ferromagnetic above 0.2 ML with its magnetic easy axis canted from surface normal direction. As temperature is increased near the Curie temperature, there is an irreversible spin reorientation to the perpendicular out-of-plane direction. The canting can be understood as arising from a competition between an in-plane, step-induced magnetic anisotropy and a perpendicular surface anisotropy associated with extended terraces due to the polarization of the proximal Pt. Above 1.7 ML the perpendicular easy axis reorients to in-plane, along the step direction, due to the dominance of the shape anisotropy. The magnetic anisotropy energy is extracted by fitting the temperature dependence of the coercivity data.