An anti-icing system for a turbine engine vane extending between an outer casing and an inner casing defining a passage, the system includes an injector device for injecting a jet of air into the passage upstream from the vane, the injector device including a first injection orifice for injecting the jet of air, the first orifice passing through one member selected from the outer casing and the inner casing, and being located in such a manner that, at a first speed of the engine wherein a stream of air flows generally in the passage along a first direction, the first orifice and a leading edge of the vane are substantially in alignment along the first direction, the first orifice is spaced apart from the junction between the leading edge of the vane and the member through which the first orifice passes by a distance of at least 10 mm, and preferably of about 15 mm.