The magnetic dipole collective excitation, known as scissors mode, is studied in odd deformed nuclei within the framework of a particle-core coupling scheme. The description is made in the intrinsic and laboratory frames. In both frames the core is described in the RPA approach by a schematic many body Hamiltonian. In the intrinsic frame we use an effective particle-core Hamiltonian which is treated perturbatively. In the laboratory frame twoK=1/2 triplets withJ=1/2, 3/2, 5/2 are constructed through projection from two intrinsic excited states respectively. Each member of these multiplets are collectivelyM1 excited from the state (K, Jπ)=(3/2, 3/2+). Their energies are obtained by averaging a rotationally invariant Hamiltonian. Another multiplet withK=3/2 andJ=3/2, 5/2, which is strongly coupled to the state (K, Jπ)=(5/2, 5/2+) through aM1 transition, is described. These results indicate that theM1 collective excitation should exist also in odd deformed nuclei.