We use direct numerical simulations to study the dynamics of incom-pressible homogeneous turbulence subjected to a uniform magnetic field B in a rotating frame with rotation vector. We consider two cases: B and ⊥ B. The initial state is homogeneous isotropic hydrodynamic turbulence with Reynolds number Re = u l l/ν 170. The magnetic Prandtl number Pm = ν/η = 1 and the Elsasser number = B 2 /(2 η) = 0.5, 0.9 or 2. For both the cases B and ⊥ B, the total energy decays as ∼ t −5/7 for = 0.5 and 0.9, and as ∼ t −6/7 for = 2. In the spectral range 2 < k < 20, the kinetic energy spectrum scales as ∼ k −p where p increases with time (2 ≤ p ≤ 4.2). This scaling is similar to that observed in quasi-static MHD. The two rotating MHD flow cases differ mainly in how kinetic and magnetic fluctuations exchange energy, with a mechanism mostly driven by the dynamics of the spectral buffer layer around k = | · k|/ ≈ 0. At k = 0, the inertial and Alfvén waves frequencies vanish when B, but only the inertial waves frequency vanishes when ⊥ B. When B, rotation results in an increased reduction of magnetic fluctuations generation. In terms of anisotropy, we show that the elongated structures occurring in rapidly non-magnetised rotating flows are distorted or inhibited for ⊥ B, and weakened for B.