The support device (3) is adapted to be secured to the front face (4) of the injector, and to position an angiographic syringe (1) having a body (7) that presents an outwardly-directed projection (30), the cross-section of the body at the location of said projection being non-circular. The device which is extended forwards by a cradle (23) for supporting the syringe body, includes an upwardly-open recess (24) that presents firstly a non-circular cross-section that is complementary to a portion of the cross-section of the syringe body at the location of said projection, and secondly an abutment front face for said projection. The recess (24) includes a central portion (31) of circularly-arcuate cross-section, which portion is extended by two diametrically-opposite notches (32).