Observations of lower hybrid (LH) radio frequency heating effects on toroidal plasma rotation in L-mode Tore Supra plasmas are reported. A database of more than 50 plasma discharges has been analysed. Core rotation is found to increment in co- or counter-current direction depending on the plasma current (Ip). At low plasma current, the induced rotation is up to +15 km s−1 in the co-current direction, the rotation profile being affected over the whole plasma minor radius. At higher plasma current, an opposite trend is observed, the core plasma rotation incrementing up to −15 km s−1 in the counter-current direction, the profile being affected up to r/a < 0.6 only. At the zero crossing point, which is defined when the plasma rotation profile is not affected by LH power injection, Ip ∼ 0.95 MA. In both low and high Ip cases, rotation increments are found to increase with the injected power. Several mechanisms in competition which can induce co- or counter-current rotation in Tore Supra LHCD plasmas are investigated and typical order of magnitude are discussed. How those effects evolve with plasma parameters and how they compete are important issues addressed in this paper. Rotation increment increase with Ip at fixed LH power is consistent with a dominant standard momentum confinement mechanism related to Ip increase. The co-current change in rotation is consistent with a fast electron ripple loss mechanism, while thermal ripple induced neoclassical friction and absorbed LH wave momentum from resonant electrons are expected to influence the rotation in the counter-current direction. Finally, the numerical simulations show that the radial turbulent momentum transport does impact the rotation behaviour inducing increment in co- or counter-current directions, depending on the plasma current amplitude.