There are various types of scattering of electromagnetic wave. what type of scattering involves infrared electromagnetic wave?
The question is rather broad, so I will provide a broad answer.
It really depends on the energy level structure of the scatter (atom? molecule? free electron?). Classically, scattering happens because the incoming EM wave induces and drives an oscillating dipole moment in the scattering object, and that oscillating dipole moment radiates. The strength of the induced dipole moment depends on the polarizability of your scatterer at the incident frequency, and of course that depends on the frequency detuning between the incident frequency and the energy spacings between different states.
So what kind of energy level structure is infrared EM relevant for?
Typically, atoms have transitions in the visible to near-infrared frequency. For free electrons, there is no internal structure. But the incident EM field can oscillate the free electrons and make them radiate. At low frequency (low energy), there is Thomson scattering, and the scattering cross-section is independent of wavelength, so you can create Thomson scattering with your infrared light source. Note that Thomson scattering is the low-energy limit of Compton scattering, which happens at the relativistic scale (and requires X-ray). Finally, the vibrational energy level spacings in molecules is most likely in the infrared region, so you expect to see prominent scattering with infrared light with molecules.
There are also two prominent scattering processes: Rayleigh (elastic, final state same as initial state) and Raman (inelastic, final state different from initial state). There is also Bragg scattering, which refers to the change in the final external state (external meaning motional), whereas Raman usually refers to change in the internal state. Raman scattering is an invaluable tool for studying molecules.