We consider a hot plasma, with two ion species, in which the minority ion species has an anisotropic temperature with T_{perpendicular to}>T_//. The conditions for the occurrence of the electromagnetic ion cyclotron instability are obtained within a uniform plasma model. Two regimes of instability are identified, the first for frequencies close to the minority ion cyclotron frequency and the second for frequencies below the majority ion cyclotron frequency. The second instability occurs for a lower value of T_{perpendicular to}/T_// but the first instability has a much faster growth rate. We quantify how parallel propagating left circularly polarized electromagnetic waves can be driven linearly unstable, for parameter regimes which are relevant to minority ion cyclotron heating experiments in tokamak plasmas.