An applicator (7) for a cosmetic product comprising a gripping member (9), a support (11) secured to the gripping member, a rod (13), means (15) for mounting the rod on the support, and a member (17) for applying the cosmetic product borne by the rod.The support includes a guiding finger (23) extending along a longitudinal direction (L) from the gripping member. The rod defines an internal housing (53) adapted for receiving the guiding finger in a mounted configuration of the applicator, the mounting means being adapted so that the rod is freely movable in rotation relatively to the guiding finger around the longitudinal direction in the mounted configuration.An assembly including the applicator and a reservoir intended for the cosmetic product.