Understanding the origin of rotation in ion cyclotron resonance frequency (ICRF) heated plasmas is important for predictions for burning plasmas sustained by alpha particles, being characterized by a large population of fast ions and no external momentum input. The angular velocity of the plasma column has been measured in JET H-mode plasmas with pure ICRF heating both for the standard low toroidal magnetic ripple configuration, of about ~0.08% and, for increased ripple values up to 1.5% (Nave et al 2010 Phys. Rev. Lett. 105 105005). These new JET rotation data were compared with the multi-machine scaling of Rice et al (2007 Nucl. Fusion 47 1618) for the Alfvén–Mach number and with the scaling for the velocity change from L-mode into H-mode. The JET data do not fit well any of these scalings that were derived for plasmas that are co-rotating with respect to the plasma current. With the standard low ripple configuration, JET plasmas with large ICRF heating power and normalized beta, βN ≈ 1.3, have a very small co-current rotation, with Alfvén–Mach numbers significantly below those given by the rotation scaling of Rice et al (2007 Nucl. Fusion 47 1618). In some cases the plasmas are actually counter-rotating. No significant difference between the H-mode and L-mode rotation is observed. Typically the H-mode velocities near the edge are lower than those in L-modes. With ripple values larger than the standard JET value, between 1% and 1.5%, H-mode plasmas were obtained where both the edge and the core counter-rotated.