The code TORIC solves the finite Larmor radius wave equations in the ion cyclotron range of frequencies in arbitrary axisymmetric toroidal geometry. The model used, based on the finite Larmor radius approximation, describes the compressional and torsional Alfvén waves and ion Bernstein waves excited by linear mode conversion. Absorption by the ions occurs at the fundamental and first harmonic of the cyclotron frequency, and by the electrons through Landau and transit time damping. The numerical solution is based on the spectral representation of the wave fields in the poloidal angle , and cubic finite elements in the radial variable . The spectral approach in the poloidal angle allows us to evaluate in a numerically efficient way the integrals over the particle orbits along magnetic field lines which arise when the high frequency (HF) plasma current is obtained by solving the linearized Vlasov equation; the leading effects of toroidicity on cyclotron absorption and spatial dispersion are also taken into account. The code offers a number of options, which allow us to compare the complete finite Larmor radius model with simpler approximations, such as the widely used order reduction algorithm, which replaces the excitation of ion Bernstein waves with an equivalent power sink.