It has been widely accepted that the heating from the AGN feedback is the most plausible solution to the cooling flow problem in the gaseous halos of galaxy clusters, groups and giant elliptical galaxies. Besides heating the ambient gas, the mechanical jet feedback also strongly perturbs the ambient intracluster medium (ICM) and generates turbulent motions in the ICM. These perturbations trigger the development of thermal instabilities in the ICM, leading to cold gas phase precipitation out of the hot phase in the ICM. Recent observations of the velocity structure function (VSF) of cold phase ICM offers a new probe of the dynamical state of ICM. The VSF is closely related to the power spectrum of the velocity fluctuations and can be directly compared to the results from numerical simulations. Despite using various numerical methods, hydrodynamic simulations of the AGN feedback and cooling flow problem often reveal formation of a massive, long-lived cold disk in the vicinity of the central SMBH, which is inconsistent with the observations. In our previous work, we found that including weak magnetic fields prevents the formation of the disks in elliptical galaxies. This is because local B-field amplification in the precipitating cold gas leads to strong magnetic breaking, which quickly extracts angular momentum from the accreting clouds. Therefore, magnetic fields can have profound influence on the dynamics of the cold phase gas as the locally enhanced magnetic fields exert strong tension force on the precipitating cold gas. Motivated by these findings, we performed high resolution, three dimensional magnetohydrodynamic (MHD) simulations to investigate how the magnetic fields affect the morphology of the cold phase in the ICM and the ICM turbulence properties. We found that: i) while the formation of long-lived cold massive disks occurs in hydrodynamic simulations, it is prevented in the MHD cases; ii) in agreement with the observations, the slope of the VSF of cold phase ICM is steeper than that predicted from the Kolmogorov turbulence.