We have investigated the relaxation of the magnetically induced birefringence in a suspension of magnetic nanoparticles in order to detect the binding reaction of polyclonal antibodies on the particle surface. The birefringence relaxation is driven by the rotational diffusion of the complex formed by the magnetic nanoparticles bound to the antibody and thus is directly related to the hydrodynamic size of this complex. Birefringence relaxations are well described by stretched exponential laws revealing a polydisperse distribution of hydrodynamic diameters. Comparing the size distribution of samples with different initial ratios of immunoglobuline added per magnetic nanoparticles, we evidence the graft of an antibody on particle and eventually the onset of particles aggregation. Measurements on samples separated in size by gel filtration demonstrate the robustness of our experiment for the determination of size distribution and its modification due to the adsorption of a macromolecule. The immunoglobuline binding assay is performed comparatively for ionic magnetic nanoparticles with different coatings.