Optical Tweezers are well known for manipulating and tracking microscopic particles used in many biological and microfluidic applications. Trapping birefringent particles, e.g. liquid crystal droplets, gives insight into the aspect of light polarization in optical tweezers. The outstanding properties of liquid crystal droplets are their high refractive index and birefringent property suitable for light angular momentum transfer. Under the microscope, the Maltese cross of radial nematic liquid crystal droplet was observed. Trapped under 1064 nm Optical Tweezers with power lower than 80 mW, the droplet precession around the focal point of the laser beam was observed due to circular polarization of laser. In this study we show that the precession behavior of radial nematic droplet depends on the degree of ellipticity of polarization state of light, power of the laser source and size of the radial nematic droplet, affecting the induced electrical polarization and internal reordering of the droplets. The theoretical explanation and the model of this behavior have also been determined and discussed.