Oil transfer tube for a system to control the regulation of a turbine engine propeller pitch, in particular of an aircraft, the tube being intended to be mounted coaxially inside a tubular shaft of the propeller, the tube having an elongated shape and including a first male longitudinal end part intended to be inserted in a female housing of a stator casing equipped with an oil supply circuit of the tube, and a second male longitudinal end part around which is intended to be mounted a hydrodynamic bearing to guide the tube in the shaft, wherein the first end part includes a free annular end with a convex rounded cross-section intended to bear axially against an annular bottom of said housing, and in that said second end part comprises an outer axial annular bearing surface of an inner ring of the bearing, the annular bearing surface presenting in cross-section a convex curved shape.