The paper presents a study of the parametric scaling of L-mode global energy confinement times in tokamaks with plasma heating by ion cyclotron resonance frequency (ICRF) waves. A total of 292 observations from PLT, JET, ASDEX, TEXTOR, JET-2M and JIPP T-IIU, have been analysed by the multiple linear regression method. The proposed scaling of the global energy confinement time is τE ∝ a-0.2R1.3Ip1.0BT0.1κ0.2-0.1nePtot-0.5. Inspection of the residuals indicates that the ICRE discharges used in the study are well described by this scaling law. A comparison with other τE scalings based on different heating regimes was made. It appears that there is some similarity in the dependence of τE on the plasma current Ip and the absorbed total power Ptot between ICRF and NBI heating schemes. Within the experimental uncertainty, the empirical scaling law satisfies the constraints imposed by the collisionless high β model (Connor, J.W., Taylor, J.B., Nucl. Fusion 17 (1977) 1047), and it is qualitatively well linked with the mode conversion theory. In the L-mode, there is a continuous degradation of the energy confinement time with total heating power and, therefore, improvements are needed, which can be achieved by modification of either the experimental techniques or the tokamak configurations